In how many ways can 12 persons of which 3 are brothers be s... | MATH - DEFINITON OF COMBINATIONS, CONDITION COMBINATIONS, DIVISION INTO GROUPS, DERANGEMENTS | SolveeIt | Solveeit

Today, August 23

Question

In how many ways can 12 persons of which 3 are brothers be seated in a row so that the borthers are never together.

A

∠3 ∠10

B

∠3 $10P_{3}$

C

∠10 $10P_{3}$

D

∠9 ¹⁰P₃

Answer

∠9 ¹⁰P₃

Explanation

Solution

9 persons can be arranged in ∠9 ways. In the ten gaps between 9 persons, 3 brothers can be arranged in ¹⁰P₃ ways.

Total no. of arrangements = ∠9, ¹⁰P₃.