QUESTION

CSAT

Easy

Maths

Prelims 2023

There are five persons, P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done?

Select an option to attempt

Explanation

There are five tasks that need to be assigned to five persons. Here two cases are possible. Case 1: Task-2 is assigned to R Case 2: Task-2 is assigned to S

Tasks	Case 1	Case 2
1	S or T. So, $2$ possible ways	R or T. So, $2$ possible ways
2	R	S
3	3 possible ways	3 possible ways
4	2 possible ways	2 possible ways
5	1 possible way	1 possible way

In Case 1, total number of possible ways = $2 \times 1 \times 3 \times 2 \times 1 = 12$ ways In Case 2, total number of possible ways = $2 \times 1 \times 3 \times 2 \times 1 = 12$ ways So, the assignment can be done in $12 + 12 = 24$ ways.