Question

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 there are at least two consonants immediately following each vowel? (c) In how many different ways can 2n students be paired up? (d) Two -digit sequences of digits 0,1,...,9 are said to be of the same type if the digits of one are a permutation of the digits of the other. For n -8, for example, the sequences 03088 929 and 00238899 are the same type. How many types of n-digit sequences are there?

Answer 1

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d) Apologies but T Althaugh using a urable to sAveo this aððie a才a Soluttn.YU-by , try to solveeurth。