Find the number of 4 letter words using the letters of the word KRISHNA in which at least one letter is repeated

Find the number of 4 letter words using the letters of the word KRISHNA in which at least one letter is repeated

A
$7^{4}$
B
${}^{7}P_{4}$
C
$4^{7}$
D
$T^{4} - {}^{7}P_{4}$

Solution:

Given KRISHNA

Here $n = 7, r = 4$

At least one letter is repeated $= n^{r} -^{n} P_{r}$ $= 7^{4} -^{7} P_{4}$

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