How many numbers can be formed from the digit | vedclass

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Question

(D) The total number of numbers that can be formed using the digits $1, 2, 3, 4$ without repetition includes $1$-digit,$2$-digit,$3$-digit,and $4$-dig

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The total number of numbers that can be formed using the digits $1, 2, 3, 4$ without repetition includes $1$-digit,$2$-digit,$3$-digit,and $4$-digit numbers.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 $= ^4P_4 = 4 	imes 3 	imes 2 	imes 1 = 24$.Total numbers $= ^4P_1 + ^4P_2 + ^4P_3 + ^4P_4 = 4 + 12 + 24 + 24 = 64$.Thus,the correct option is $D$.

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

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