There are 5 letters and 5 directed envelopes. | vedclass

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(B) The total number of ways to arrange $5$ letters in $5$ envelopes is given by $5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.In these $120$ way

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$119$

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(B) The total number of ways to arrange $5$ letters in $5$ envelopes is given by $5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.In these $120$ ways,there is exactly $1$ way where every letter is placed in its correct (directed) envelope.The question asks for the number of ways such that all letters are not put in their directed envelopes. This is equivalent to finding the total number of permutations minus the case where all letters are in their correct envelopes.Number of ways $= 120 - 1 = 119$.

There are $5$ letters and $5$ directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes?

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