How many 3-digit numbers are there,with disti | vedclass

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(C) The set of odd digits is ${1, 3, 5, 7, 9}$.There are $5$ such digits available.To form a $3$-digit number with distinct digits,we need to select a

Vedclass · Accepted Answer

$60$

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(C) The set of odd digits is ${1, 3, 5, 7, 9}$.There are $5$ such digits available.To form a $3$-digit number with distinct digits,we need to select and arrange $3$ digits out of these $5$ available odd digits.The number of ways to do this is given by the permutation formula $P(n, r) = \frac{n!}{(n-r)!}$,where $n=5$ and $r=3$.Alternatively,using the fundamental principle of counting:The first digit can be chosen in $5$ ways.The second digit can be chosen in $4$ ways (since digits must be distinct).The third digit can be chosen in $3$ ways.Total number of $3$-digit numbers $= 5 	imes 4 	imes 3 = 60$.

How many $3$-digit numbers are there,with distinct digits,where each digit is odd?

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