There are three rows with three seats in each row Four boys and two girls are to be seated in these ...........

Quantitative Aptitude ( CCS) Permutation & Combination

There are three rows with three seats in each row. Four boys and two girls are to be seated in these three rows such that girls always sit in the last row. In how many ways the students can be seated?

3490

5040

2880

4560

None of these

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Explanation:

Total students = 6, 4 boys and 2 girls.

There will be two cases

Students sitting in last row	Ways to seat girls	Ways to seat boys
Case I: Only two girls	3 × 2	⁶C₄ × 4!
Case II: Two girls and 1 boy	3!	⁶C₃ × 3!

Case I: only two girls in last row, number of ways to seat two girls on three seats = 3 × 2 Now, 4 boys are to be seated on 4 seats out of six seats Number of ways = ⁶C₄ × 4!

Total ways = 3 × 2 × ⁶C₄ × 4! = 2160

Case II: Two girls and one boy in last row, number of ways to select one boy out of 4 = ⁴C₁

Number of ways to arrange two girls and one boy in last row = 3! Now, 3 boys are to be seated on 3 seats out of 6 seats

Number of ways = ⁶C₃ × 3!

Total ways = ⁴C₁ × 3! × ⁶C₃ × 3! = 2880

Total ways = (2160 + 2880) = 5040

Hence, option B is correct