Question

discrete math box answers

do a-d please

4. Hexadecimal numbers are made using the sixteen digits 0, 1, 2,3, 4, 5,6,7,8,9, A, B, C, D, E, F a) How many 5 digit hexadecimal numbers are there that do not start with the digit 07 b) How many 5 digit hexadecimal numbers that do not start with the digit 0 and do not end with the digit 0? c) How many 5 digit hexadecimal numbers start with a letter or end with a letter? w many 5 digit hexadecimal numbers where all digits are consecutive? E.g. 01234, 89ABC,

Answer 1

We have make five digits number that do not store with digit zero so first place has, 15 choices and remaining each place has 16 choices i. e, 15 16 16 16 16 Rightarrow 15 times 16^4 number of 5 digit hexadecimal number similarly do not start with zero and do not end with zero Rightarrow Fist and root place has 15 choices are remains has 16 Rightarrow 15 16 16 16 15 Rightarrow 15^2 times 16^3 Rightarrow 15^2 times 16^3 number of hexadecimal numbers with end and start with zero Firstly there are 16^5 total number of 6 5 digit hexadecimal numbers we have to find number of number with start or with letter so, Total number of hexadecimal number not end not start with letters = 15^2 times 16^3 Rightarrow (Total number of hexadecimal number start or end with letter) = 16^5 - (15^2 times 16^2) = 16^3 (16^2 - 15^2)