Question

if 4 women and 6 men sit in a bench, find the probability that none women sit side by side.
Answer with steps ​

Answer 1

Answer:

Probability = 1/6.

Step-by-step explanation:

$0 |x| 0 |x| 0 |x| 0 |x| 0 |x| 0 |x| 0$

Let x represents the position of men.

Therefore, places for women will be alterternate which is denoted by 0.

now 6 men can sit in 6! ways

and out of available 7 places, 4 women can sit in

7P_4 ways.

Therefore, total no. of ways = 6! × 7P_4

= ( 6! ) × ( 7! ÷ 3!)

= ( 6×5×4×3×2×1 ) × ( 7×6×5×4×3×2×1) ÷ (3×2×1)

= 720 × 840

= 604800

4 women and 6 men can sit in (4 + 6)! = 10! ways.

= 3628800 ways.

Therefore,

required probability = 604800/3628800

= 1/6.

Hence, the required probability = 1/6.