Permutations & Combinations
Arrangements in Queue
MMTS_Full_Test_12
Grade 12
Question:
Let $n$ be the number of ways in which 5 boys and 5 girls can stand in a queue such that all girls stand consecutively. Let $m$ be the number of ways such that exactly four girls stand consecutively. Then $\dfrac{m}{n}$ is
$\dfrac{7}{5}$
$\dfrac{5}{2}$
$\dfrac{1}{24}$
$5$
Step-by-Step Solution
Key Concept: $n$: treat 5 girls as block; $m$: choose which 4 girls are consecutive, exclude all-5-consecutive
$n=6!\cdot 5!$. $m=\binom{5}{1}\cdot 4!\cdot 7!-2\cdot 6!\cdot 5!$... $m/n=5/2$.
Correct Answer: 2