The number of permutations of n different things taking r at a time wh

1.	The number of permutations of n different things taking r at a time when 3 particular things are to be included is :A. n - 3Pr - 3 B. n – 3Pr C. nPr - 3 D. r! n – 3Cr – 3
Answer» Option : (D) Primarily, Excluding the 3 things which are to be included, we have to select (r - 3) things from (n - 3), this can be done in ^{n – 3}C_{r – 3} ways. Now, The 3 particular things can be selected from 3 remaining things only in 1 way. And the selected r things can be arranged in r! ways. So, The number of permutations of n different things taking r at a time when 3 particular things are to be included is = r! ^{n – 3}C_{r – 3}.

The number of permutations of n different things taking r at a time when 3 particular things are to be included is :A. n - 3Pr - 3 B. n – 3Pr C. nPr - 3 D. r! n – 3Cr – 3

Answer»

Option : (D)

Primarily,

Excluding the 3 things which are to be included, we have to select (r - 3) things from (n - 3), this can be done in ^{n – 3}C_{r – 3} ways.

Now,

The 3 particular things can be selected from 3 remaining things only in 1 way.

And the selected r things can be arranged in r! ways.

So,

The number of permutations of n different things taking r at a time when 3 particular things are to be included is = r! ^{n – 3}C_{r – 3}.