Question

In a college classroom some chairs are designed for lef-handers. Suppose this classroom has 20 chairs, and 8 of them are made for lefies. If 5 students randomly select chairs and sit on them in this classroom, what is the probability that at least 4 of those selected will be seats for lefies?

Answer 1

Answer: 0.0578

Explanation:

Given : Number of chairs = 20

Number of chairs made for lefties =8

Number of chairs made for righties= 20-8=12

Now, total number of way for selecting 5 chairs from 20 =
`^(20)C_5=(20!)/(5!(20-5)!)`

`=(20*19*18*17*16*15!)/((120)15!)=15504`

`[\because\ ^nC_r=(n!)/(r!(n-r)!)]`

Number of ways to select at least 4 seats for lefies :-

`^8C_4*^(12)C_1+^8C_5* ^(12)C_0\\\\=(8!)/(4!4!)\cdot12+(8!)/(5!3!)(1)=896`

Now, the probability that at least 4 of those selected will be seats for lefties :-

`(896)/(15504)=0.0577915376677\approx0.0578`

hence, the required probability = 0.0578