The number of ways of forming a queue of 4 bo | vedclass

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Question

(D) Total number of people = $4 	ext{ boys} + 3 	ext{ girls} = 7 	ext{ people}$.
Total ways to arrange $7$ people in a queue = $7! = 5040$.
To fi

Vedclass · Accepted Answer

$4320$

Vedclass · Answer

(D) Total number of people = $4 	ext{ boys} + 3 	ext{ girls} = 7 	ext{ people}$.
Total ways to arrange $7$ people in a queue = $7! = 5040$.
To find the number of ways where all girls are not together, we use the complement method: $	ext{Total ways} - 	ext{Ways where all girls are together}$.
Treating the $3$ girls as a single unit, we have $4 	ext{ boys} + 1 	ext{ unit} = 5 	ext{ units}$.
These $5$ units can be arranged in $5!$ ways, and the $3$ girls within their unit can be arranged in $3!$ ways.
Ways where all $3$ girls are together = $5! 	imes 3! = 120 	imes 6 = 720$.
Therefore, the number of ways where all girls are not together = $5040 - 720 = 4320$.

The number of ways of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is:

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