Question

There are 3 different jobs in an office. 3 women and 5 men have attended before the selection committee. If each is eligible for all jobs and at least one woman must be selected, the number of ways of allotting the 3 jobs is

• A. 46
• B. 276
• C. 138
• D. 74 \bigskip

Hint:

In restriction problems, it is often easier to compute complement cases.

Answer 1

The Correct Option is B

Concept: This is a permutation with restriction problem. First find total arrangements, then subtract invalid cases.

Step 1: Total ways without restriction.
Choose and assign 3 persons from 8: \[ {}^{8}P_{3}=8\times7\times6=336 \]

Step 2: Subtract all-men cases.
If no woman is selected, all are men: \[ {}^{5}P_{3}=5\times4\times3=60 \]

Step 3: Apply restriction.
\[ 336-60=276 \] \[ \boxed{276} \] Hence correct option: \[ \boxed{(B)}. \]