Seeking Admission in school

Probability Level 2

Three children,each accompanied by a guardian seek admission in a school .The principal wants to interview all the 6 persons one after the other subject to the condition that no child is interviewed before its guardian . In how many ways can this be done ?

120 180 90 60

2 solutions

Nguyen Thanh Long
Jun 15, 2014

The result is number of permutations of (1,2,3,4,5,6) (6 people) divides by 2x2x2. Hence the result is: $\boxed{90}$

@Cccc Dddd can you explain further ?

Anish Kelkar - 6 years, 11 months ago

Chew-Seong Cheong
Aug 6, 2014

Cccc Dddd is correct. I used logical thinking and get the same answer consider all the possible cases. The explanation is here.

All the possible ways $N=6!=720$ . In half of $N$ ways, a child is being interviewed before the guardian and the other half of $N$ , the guardian before the child. Since there are three children, $N$ has to be divided by $2^3$ to arrive at the required answer $\frac{N}{2^3}=\frac{720}{8}=\boxed{90}$ .

Seeking Admission in school

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