Question

Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object always occurs

Answer 1

Here n = 11, r = 4

One particular thing always occur:

The number of permutations = r × ^n–1P_r–1

Putting r = 4, n = 11, we get the number of permutations

= `4 xx ^((11-1))"P"_((4-1))`

= 4 × ¹⁰P₃

= `4 xx (10!)/(7!)`

= 4 × 10 × 9 × 8

= 2880