First slide

Permutations

Question

Ten letters of an alphabet are given. Words with five letters are formed by these given letters. Then the number of words which have at least one letter repeated is

Moderate

A

69760
B

30240
C

99748
D

none of these

Solution

Number of five letter words that can be formed from $10$ letters
$= 10 \times 10 \times 10 \times 10 \times 10 = 10^{5}$
Number of five letter words that have none of their letter repeated
$=^{10} P_{5} = 10 \times 9 \times 8 \times 7 \times 6 = 30240$
$∴$ Number of words which have at least one letter repeated
$= 10^{5} - 30240 = 69760$

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