Question:
Ten different letters of an alphabet are given, Words with five letters are formed from these given letters. The number of words which have at least one of their letter repeated is
Ten different letters of an alphabet are given, Words with five letters are formed from these given letters. The number of words which have at least one of their letter repeated is
Updated On: Mar 29, 2024
- $69760$
- $30240$
- $99748$
- none of these
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The Correct Option is A
Solution and Explanation
Reqd. number of ways $=10^{5}-\,10p_{5}$
$=100000-10\times9\times8\times7\times6$
$=100000-30240=69760$.
$=100000-10\times9\times8\times7\times6$
$=100000-30240=69760$.
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects