A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a choir be formed if both siblings cannot be selected together?

Answer Choices

Correct answer marked below

360

720

1120

Correct

2400

26880

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Explanation

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Official Explanation

Official

Method 1:

We need 4 children who must come from 4 different sibling pairs.

Step 1: Select 4 sibling pairs from 8 pairs =

\binom{8}{4}

ways = 70.

Step 2: Select one child from each selected sibling pair =

2 \times 2 \times 2 \times 2 = 16

ways.

Total ways =

70 \times 16 = 1120

.

Answer: Option C.

Method 2:

First child may be chosen in 16 ways.

Second child may be chosen in 14 ways (leaving the selected child and his/her sibling).

Third child may be chosen in 12 ways (leaving the selected children and their siblings).…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.