Question

Let 13 seats in a straight line are to be occupied by 4 persons. The number of
ways in which there should be exactly four empty seats between two particular
persons is-
O 15 (^6C3)
O 30 (^6C3)
O 16 (^7C2)
O 32 (^7C2)​

Answer 1

Given :  13 seats in a straight line are to be occupied by 4 persons.

To Find : The number of ways in which there should be exactly four empty seats between two particular persons is-

15 (⁶C₃)

30 (⁶C₃)

16 (⁷C₂)

32 (⁷C₂)​

Solution:

2 Particular persons can take seats in

1  , 6  

2 , 7

3 , 8

4 , 9

5 , 10

6 , 11

7 , 12

8 , 13

There are 8 ways  in each case 2 person can seat  in 2!  = 2 ways

Hence 8 x 2  = 16 ways

After this 7 seats remains   and 2 person can be selected in ⁷C₂ ways

and these two person can sit in 2!  = 2 Ways

Hence total number of arrangement = 16 * 2 * ⁷C₂

= 32 * ⁷C₂

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