Number of ways in which 3 boys and 3 girls (all are different heights) can be arranged in a line so that boys as well as girl among themselves are in decreasing order of their height (from left)

Question

Number of ways in which 3 boys and 3 girls (all are different heights) can be arranged in a line so that boys as well as girl among themselves are in decreasing order of their height (from left) (A) 6 ! (B) 3 ! × 3! × 2 ! (C) 10 (D) 20

Tardigrade Admin · Accepted Answer

Since order of the boys and girls are to be maintained in any of the different arrangements ∴ Required number =(6 !/3 ! × 3 !)=20

Q. Number of ways in which $3$ boys and $3$ girls (all are different heights) can be arranged in a line so that boys as well as girl among themselves are in decreasing order of their height (from left)

$6!$

$3! \times 3! \times 2!$

$10$

$20$

Since order of the boys and girls are to be maintained in any of the different arrangements
$∴$ Required number $= \frac{6 !}{3 ! \times 3 !} = 20$

Q. Number of ways in which 3 boys and 3 girls (all are different heights) can be arranged in a line so that boys as well as girl among themselves are in decreasing order of their height (from left)

6!

3!×3!×2!

10

20