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There are 4 women P, Q, R, S and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one women and one man. P is not to be paired with Z, and Y must necessarily be paired with some. In how many ways can 4 such pairs be formed?

There are 4 women P, Q, R, S and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one women and one man. P is not to be paired with Z, and Y must necessarily be paired with some. In how many ways can 4 such pairs be formed? Correct Answer 78

If P is paired with y; they

Q has 4 choices

R has 3 choices

S has 2 choices

Total 24 choices

(Or)

If Q is paired with y;

Then

P has 3 choices

R has 3 choices

S has 2 choices

Total 18 choices

(Or)

If R is paired with y; then

P has 3 choices

Q has 3 choices

S has 2 choices

Total 18 choices

(Or)

If S is paired with y; then

P has 3 choices

Q has 3 choices

S has 2 choices

Total 18 choices

∴ Total number of ways = 24 + 18 + 18 + 18 = 78

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