Q56 / 160 · AP EAMCET 2019 (20 Apr Shift 2) · Mathematics

A person invites 8 guests to a dinner and places 5 of them at one table and the remaining 3 at another, both the tables being round. The number of ways in which the guests can be arranged is

  • A
    40320
  • Correct answer
    B
    2688
  • C
    8064
  • D
    13440

Solution

The number of ways to select 5 person out of 8 is ${ }^8 C_5$. Now, number of ways to place 5 on round table is 4 ! and number of ways to place 3 on round table is 2 !. So, required number of ways $={ }^8 C_5 \times 4 ! \times 2 !$ $$ =\frac{8 \times 7 \times 6}{3 \times 2} \times 4 \times 3 \times 2 \times 2=42 \times 64=2688 $$ Hence, option (b) is correct.

Hence, the correct answer is option: 'B'.

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