Question

the number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is?

Answer 1

2016 answer. 4(9P3) where p is permutation

Answer 2

Answer:

So, Required number of ways = 2016

Step-by-step explanation:

Number of different things = 10

Numbers of things which are taken at a time = 4

Now, it is said that one particular thing always occur.

So The question reduces to selecting 9 things from the 3 things

This can be done easily by using the concept of combinations

Number of ways selecting 3 things out of 9 different things such that one particular thing always occur =

$_{3}^{9}\textrm{C}=\frac{9!}{3!\times 6!}=84$

Now, the 4th thing is fixed so number of ways for selecting the 4th thing = 4! = 24

So, Required number of ways = 84 × 24 = 2016