How many different signals can be transmitted | vedclass

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(D) The total number of flags is $n = 3 + 2 + 2 = 7$.Since the flags of the same color are identical,we use the formula for permutations of objects wh

Vedclass · Accepted Answer

$210$

Vedclass · Answer

(D) The total number of flags is $n = 3 + 2 + 2 = 7$.Since the flags of the same color are identical,we use the formula for permutations of objects where some are alike:Number of signals $= \frac{n!}{p_1! p_2! p_3!}$Here,$p_1 = 3$ (red),$p_2 = 2$ (yellow),and $p_3 = 2$ (green).Number of signals $= \frac{7!}{3! 2! 2!} = \frac{7 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1}{(3 	imes 2 	imes 1) 	imes (2 	imes 1) 	imes (2 	imes 1)}$$= \frac{5040}{6 	imes 2 	imes 2} = \frac{5040}{24} = 210$.Thus,the total number of different signals is $210$.

How many different signals can be transmitted by arranging $3$ red,$2$ yellow and $2$ green flags on a pole? [Assume that all the $7$ flags are used to transmit a signal.]

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