Question

7 people leave their bags outside temple and returning after worshiping the deity picked one bag each at random. In how many ways at least one and at most three of them get their correct bags?

• A. ⁷C₃ .9 + ⁷C₅ .44 + ⁷C₁ .265
• B. ⁷C₆ .265 + ⁷C₅ .9 + ⁷C₇ .44
• C. ⁷C₅ .9 + ⁷C₂ .44 + ⁷C₁ .265
• D. None of these

Answer 1

Answer: (A)

⁷C₃ .9 + ⁷C₅ .44 + ⁷C₁ .265

Answer 2

No. of ways getting one correct

= ⁷C₁ 6! $\left( 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + ... + \frac{1}{6!} \right)$

= ⁷C₁.265

No. of ways getting two correct

= ⁷C₂. 5! $\left( 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + ... - \frac{1}{5!} \right)$

= ⁷C₂ . 44

No. of ways getting three correct

= ⁷C₃.4! $\left( 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} \right)$

= ⁷C₃.9

Required no. of ways

= ⁷C₃ . 9 + ⁷C₂ . 44 + ⁷C₁. 265