Question

(ix) 8 persons are to be arranged in a row. What is the probability that there are
exactly 3 persons between two particular persons A and B.
(a) 1/7
(b) 1/6
(c) 1/5
(d) none of these
probability​

Answer 1

Answer:

• first step is know that A,B,C is a group of 3 persons
• which is any 3 people out of 6 people because A and B is fix corner

know we set arrangement :

1. 2 person a and b is have two choice for corner stands beside of three person = 2!
2. between A and B any 3 person seat out of 6 people = 6ce
3. three person is changing their standings with each other = 3!
4. last possible arrangement is group of 5 person with other three = 4!

Answer = 2! ×3!×4!×⁶c3

= 2×6×24×20

= 5760

total number of ways = 8! = 40320

p (A) = 5760/40320 = 1/7

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