Question

A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least 4 of them are in wrong envelopes?

• A. 72
• B. 719
• C. 664
• D. 135

Answer 1

Answer: (C)

664

Answer 2

no. of ways = ⁶C₂.4! $\left( 1 - \frac{1}{1!} + ... + \frac{1}{4!} \right)$

+ ⁶C₁.5! $\left( 1 - \frac{1}{1!} + ... - \frac{1}{5!} \right)$ + ⁶C₀ . 6! $\left( 1 - \frac{1}{1!} + .... + \frac{1}{6!} \right)$

= 135 + 264 + 265 = 664