The number of sequences of ten terms,whose te | vedclass

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(C) We need to form a sequence of $10$ terms using the digits $0, 1, 2$ such that there are exactly five $1$s,three $2$s,and consequently two $0$s $(1

Vedclass · Accepted Answer

$2520$

Vedclass · Answer

(C) We need to form a sequence of $10$ terms using the digits $0, 1, 2$ such that there are exactly five $1$s,three $2$s,and consequently two $0$s $(10 - 5 - 3 = 2)$.This is a problem of permutations of a multiset where the items are not all distinct.The number of ways to arrange $5$ ones,$3$ twos,and $2$ zeros is given by the multinomial coefficient:$	ext{Number of sequences} = \frac{10!}{5! 	imes 3! 	imes 2!}$Calculating the value:$\frac{10 	imes 9 	imes 8 	imes 7 	imes 6 	imes 5!}{5! 	imes (3 	imes 2 	imes 1) 	imes (2 	imes 1)} = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{6 	imes 2} = 10 	imes 9 	imes 4 	imes 7 = 2520$.

The number of sequences of ten terms,whose terms are either $0$,$1$,or $2$,that contain exactly five $1$s,exactly three $2$s,and two $0$s,is equal to:

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