CA Foundation · Quantitative Aptitude · Seating Arrangements
In how many ways can 3 men and 3 women be seated in a row of six chairs so that men and women occupy alternate seats?
The number of ways is 72. Alternate seating can start with a man or a woman, giving two patterns. In each pattern the three men can be arranged in 3! ways and the three women in 3! ways, so the total is 2 × 6 × 6 = 72.
- A36
- B72Correct
- C144
- D720
Explanation
There are two possible patterns: the row starts with a man (M W M W M W) or with a woman (W M W M W M). For each pattern, the men can be arranged in 3! = 6 ways and the women in 3! = 6 ways, giving 36 arrangements. With 2 patterns, the total is 2 × 36 = 72. The answer 36 is wrong because it counts only one of the two patterns.
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