The number of four-digit numbers that can be | vedclass

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Question

(B) To find the number of four-digit numbers with at least two identical digits,we subtract the number of four-digit numbers with all distinct digits

Vedclass · Accepted Answer

$505$

Vedclass · Answer

(B) To find the number of four-digit numbers with at least two identical digits,we subtract the number of four-digit numbers with all distinct digits from the total number of possible four-digit numbers.$1$. Total number of four-digit numbers using the digits $1, 2, 3, 4, 5$ (repetition allowed) is $5 	imes 5 	imes 5 	imes 5 = 5^4 = 625$.$2$. Number of four-digit numbers with all distinct digits (no repetition) is $5 	imes 4 	imes 3 	imes 2 = 120$.$3$. Number of four-digit numbers with at least two identical digits = (Total numbers) - (Numbers with all distinct digits).$= 625 - 120 = 505$.

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ in which at least two digits are identical is

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