4. How many sequences of length 6 formed from the 26 letters without repetition are there...
4. How many sequences of length 6 formed from the 26 letters
without repetition are there where the vowels (a,e,i,o,u) may only
appear in the first or/and last positions (possibly
neither)?
Homework Answers
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4. How many sequences of length 6 formed from the 26 letters without repetition are there...
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2,...
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2, 3, 4, 5, 7 and 9 if digits may not be repeated? (ii) How many of the numbers so formed are even? (iii) How many of the numbers formed are divisible by 3? (iv) How many of the numbers formed are less than 700,000? (b) JACK MURPHY’s seven character password consists of four let- ters chosen from the ten letters in his name (all...
4. (HHM Problem 2.1 #2) Assume that a vowel is one of the five letters A,...
4. (HHM Problem 2.1 #2) Assume that a vowel is one of the five letters A, E, I, O, or U. (a) How many eleven-letter sequences from the alphabet contain exactly three vowels? (b) How many of these have at least one repeated letter?
How many 4-digit numbers can be formed using only the digits {1,2,3} if repetition is allowed...
How many 4-digit numbers can be formed using only the digits {1,2,3} if repetition is allowed and the number must contain the digit 3 somewhere. Hint: it may be easier to first count the numbers that don't contain the digit 3.
How many three-letter "words" can be made from 6 letters "FGHIJK" if repetition of letters (a)...
How many three-letter "words" can be made from 6 letters "FGHIJK" if repetition of letters (a) is allowed? An access code consists of 1 letter of the alphabet followed by 6 digits. (Digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.) How many different access codes are possible? A jar contains 9 red marbles, numbered 1 to 9, and 12 blue marbles numbered 1 to 12. a) A marble is chosen at random. If you're told the...
Problem1 Answer the following questions with a number or a simple formula involving factorials an...
6.042 - 1
Problem1 Answer the following questions with a number or a simple formula involving factorials and binomial coef. ficients. Briefly explain your answers. (a) How many ways are there to order the 26 letters of the alphabet so that no two of the vowels a, e, i, o, u appear consecutively and the last letter in the ordering is not a vowel? Hint: Every vowel appears to the left of a consonant ters of the alphabet so that...
How many 6-letter code words can be formed from the letters T, O, U, DL, Y...
How many 6-letter code words can be formed from the letters T, O, U, DL, Y if no letter is repeated? If letters can be repeated? If adjacent letters must be different? There are possible 6-letter code words if no letter is repeated. (Type a whole number.) There are possible 6-letter code words if letters can be repeated. (Type a whole number) There are possible 6-letter code words if adjacent letters must be different. (Type a whole number.)
can you try these I do not know if they are correct (from e-h mainly) please...
can you try these I do not know if they are
correct
(from e-h mainly)
please check the others if you have the time to
The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and sometimes y). Suppose we randomly select 8 letters from the alphabet without replacement. Let X = the number of vowels chosen (including y as a vowel). a. How many possible ways are there to select the 8 out of...
How many different passwords of size 6 can be formed using English alphabet characters if the...
How many different passwords of size 6 can be formed using English alphabet characters if the first letter must be a capital letter and the remaining letters must be lower case? a) 26 * C(25, 5) b) P(26, 5) c) 26 * P(26, 5) d) 26 * C(26, 5) e) P(26, 6)
How many unique codes are possibly formed from two characters, where the first character can be...
How many unique codes are possibly formed from two characters, where the first character can be 4 to 6, and the second character can be C to H?
animali 32. How many strings of six lowercase letters from the En- glish alphabet contain IS...
animali 32. How many strings of six lowercase letters from the En- glish alphabet contain IS a) the letter a? b) the letters a and b? Osadno-o lls i d c) the letters a and b in consecutive positions with a preceding b, with all the letters distinct?) d) the letters a and b, where a is somewhere to the left of b in the string, with all the letters distinct? into
4. (HHM Problem 2.1 #2) Assume that a vowel is one of the five letters A, E, I, O, or U. (a) How many eleven-letter sequences from the alphabet contain exactly three vowels? (b) How many of these have at least one repeated letter?
6.042 - 1
Problem1 Answer the following questions with a number or a simple formula involving factorials and binomial coef. ficients. Briefly explain your answers. (a) How many ways are there to order the 26 letters of the alphabet so that no two of the vowels a, e, i, o, u appear consecutively and the last letter in the ordering is not a vowel? Hint: Every vowel appears to the left of a consonant ters of the alphabet so that...
How many 6-letter code words can be formed from the letters T, O, U, DL, Y if no letter is repeated? If letters can be repeated? If adjacent letters must be different? There are possible 6-letter code words if no letter is repeated. (Type a whole number.) There are possible 6-letter code words if letters can be repeated. (Type a whole number) There are possible 6-letter code words if adjacent letters must be different. (Type a whole number.)
can you try these I do not know if they are
correct
(from e-h mainly)
please check the others if you have the time to
The English alphabet has 26 letters. There are 6 vowels. (a, e, i, o, u, and sometimes y). Suppose we randomly select 8 letters from the alphabet without replacement. Let X = the number of vowels chosen (including y as a vowel). a. How many possible ways are there to select the 8 out of...
animali 32. How many strings of six lowercase letters from the En- glish alphabet contain IS a) the letter a? b) the letters a and b? Osadno-o lls i d c) the letters a and b in consecutive positions with a preceding b, with all the letters distinct?) d) the letters a and b, where a is somewhere to the left of b in the string, with all the letters distinct? into
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