How many necklaces can be formed by selecting | vedclass

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(B) Step $1$: Select $4$ glass beads from $6$ available: $^6C_4 = 15$ ways.Step $2$: Select $4$ metal beads from $5$ available: $^5C_4 = 5$ ways.Step

Vedclass · Accepted Answer

$^6C_4 	imes ^5C_4 	imes \frac{7!}{2!}$

Vedclass · Answer

(B) Step $1$: Select $4$ glass beads from $6$ available: $^6C_4 = 15$ ways.Step $2$: Select $4$ metal beads from $5$ available: $^5C_4 = 5$ ways.Step $3$: Total beads selected = $4 + 4 = 8$ beads.Step $4$: The number of ways to arrange $n$ distinct beads in a necklace is $\frac{(n-1)!}{2}$.Step $5$: For $8$ beads,the number of arrangements is $\frac{(8-1)!}{2} = \frac{7!}{2!}$.Step $6$: Total number of necklaces = $^6C_4 	imes ^5C_4 	imes \frac{7!}{2!}$.

How many necklaces can be formed by selecting $4$ beads from $6$ different colored glass beads and $4$ beads from $5$ different colored metal beads?

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