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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$60$

Vedclass · Answer

(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?

Similar Questions

In an election there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of arrangements is

In how many different ways can the letters of the word '$BANKING$' be arranged so that the vowels always come together?

Assuming the balls to be identical except for the difference in colours,the number of ways in which one or more balls can be selected from $10$ white,$9$ green,and $7$ black balls is:

How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word $MEDITERRANEAN$ such that the first letter is $E$ and the last letter is $R$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module