Question

In how many ways 10 persons can be arranged such that 3 are always together?

Answer 1

2 or 3 to arrange together

Answer 2

Answer:

10 persons can be arranged such that 3 are always together in 241920 ways.

Step-by-step explanation:

Given : Total no. of persons = 10

To Find : In how many ways 10 persons can be arranged such that 3 are always together?

Solution:

Three people who are always together will be considered as 1 unit

So, remaining people = 10 - 3 = 7

So, we can take total number of persons as 8

Now These 8 persons can rearranged themselves

So, No. of ways of arranging these 8 person =$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 =40320$

Now the three people who are grouped together can rearrange among themselves .

So, No. of ways three people who are grouped together can rearrange among themselves = $3! = 3 \times 2 \times 1 = 6$

So, Total no. of ways = $40320 \times 6 = 241920$

Hence 10 persons can be arranged such that 3 are always together in 241920 ways.