Question

31. Find the number of permutations of n dissimilar things taken r at a time, in
which a particular thing always occur.
​

Answer 1

Answer:

Here we have "n" things and we have to find out the permutation of "r" things take at a time such that one particular thing is always coming.

Take an example, you have letters A to Z.

Here you have to choose 10 letters such that R always comes i.e. R is fixed, so we just have 25 letters and we have to choose 9 out of them as we have already chosen one (R).

Similarly, here we have to chose (r−1) from (n−1) which can be done in

(n−1)

C

(r−1)

.

Now we have r selection which can be arranged in r! ways

(n−1)

C

(r−1)

×r!=(r)×

(n−1)

P

(r−1)

.

Step-by-step explanation:

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