Words with odd numbers of letters

Number Theory Level pending

Given the set of English alphabet (26 letters), find numbers of ways to select a set of odd number of different letters?


The answer is 33554432.

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1 solution

Ossama Ismail
Dec 6, 2016

number of ways to select one letter = 26 C 1 26 C1

number of ways to select three letters = 26 C 3 26 C3

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Number of all way to select odd number of letters = 26 C 1 26 C1 + 26 C 3 26 C3 + ...... + 26 C 25 26 C 25 = 2 25 2^{25}

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