How many numbers can be formed from the digit | vedclass

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(D) To form numbers using the digits $1, 2, 3, 4$ without repetition,we can form numbers of different lengths:- Number of $1$-digit numbers $= ^4P_1 =

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$^4P_1 + ^4P_2 + ^4P_3 + ^4P_4$

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(D) To form numbers using the digits $1, 2, 3, 4$ without repetition,we can form numbers of different lengths:- Number of $1$-digit numbers $= ^4P_1 = 4$- Number of $2$-digit numbers $= ^4P_2 = 4 	imes 3 = 12$- Number of $3$-digit numbers $= ^4P_3 = 4 	imes 3 	imes 2 = 24$- Number of $4$-digit numbers $= ^4P_4 = 4 	imes 3 	imes 2 	imes 1 = 24$Since these cases are mutually exclusive,the total number of possible numbers is the sum of these values:Total $= ^4P_1 + ^4P_2 + ^4P_3 + ^4P_4$.

How many numbers can be formed from the digits $1, 2, 3, 4$ when the repetition is not allowed?

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