The number of ways in which 6 different marbles can be put in two boxes of different sizes so that no box remains empty is
Solution
Correct Answer: Option A
If we put 1 marble in the first box and the rest in the other, then the number of ways it can be done
= 6C1 × 5C5 = 6 × 1 = 6
If we put 2 marble in the first box and the rest in the other, then the number of ways it can be done
= 6C2 × 4C4 = 15 × 1 = 15
If we put 3 marble in the first box and the rest in the other, then the number of ways it can be done
= 6C3 × 3C3 = 20 × 1 = 20
If we put 4 marble in the first box and the rest in the other, then the number of ways it can be done
= 6C4 × 2C2 = 15 × 1 = 15
If we put 5 marble in the first box and the rest in the other, then the number of ways it can be done
= 6C5 × 1C1 = 6 × 1 = 6
The number of ways that 6 different marbles can be put in boxes of different sizes so that no box remain empty is = 6 + 15 + 20 + 15 + 6 = 62
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions