Permutations

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Question

If there are 30 onto, mappings from a set containing $n$ elements to the set $\{0, 1\}$ , then n equals:

Easy

Solution

Suppose the set contains n elements.Then number of onto mappings
$= 2^{n} - 1 - 1 = 2^{n} - 2$
Thus, $2^{n} - 2 = 30 \Rightarrow n = 5$

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