Question

If X is a set containing n > 1 elements and Y is a set containing m > 1 elements. The number of relations from X to Y is –

• A. 2^mn
• B. mn
• C. 2^mn – 1
• D. None of these

Answer 1

Answer: (A)

2^mn

Answer 2

If there is no restriction, we can select 3 balls out of

(2 + 3 + 4) balls in ⁹C₃ ways. If black balls are to be excluded, this can be done in ⁶C₃ ways. Therefore the number of ways when at least on black ball is included is

⁹C₃ – ⁶C₃ = $\frac{9 \times 8 \times 7}{3 \times 2 \times 1}$ – $\frac{6 \times 5 \times 4}{3 \times 2 \times 1}$ = 84 – 20 = 64.