Question

The number of arrangements of 10 different things taken 4 at a time in which one particular
thing always occurs is
(a) 2015
(6) 2016
(c) 2014
(d) none of the​

Answer 1

Here we have to find the numbers of ways in which 4 places can be filled with 10 given objects such that a particular object occur in each arrangement.

☆ As we know that the formula used in such situations → P ( n-1, r -1) × r .

Here n = 10 and r = 4

So using this formula .

→ $\frac{(10 - 1)!}{[(10 -1 )- (4-1)]!}$× 4

→ $\frac{9!}{6!}$× 4

→ $\frac{9×8×7(6!)}{6!}$×4

→ 9 ×8×7×4

→ 2016 is the required answer .