The number of distinct positive integers that | vedclass

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

Question

(C) The given digits are $0, 1, 2, 3$. We need to form distinct positive integers using these digits at most once.Case $I$: $4$-digit integers.The fir

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(C) The given digits are $0, 1, 2, 3$. We need to form distinct positive integers using these digits at most once.Case $I$: $4$-digit integers.The first place can be filled by any of the $3$ non-zero digits $(1, 2, 3)$. The remaining $3$ places can be filled by the remaining $3$ digits in $3 	imes 2 	imes 1$ ways.Number of $4$-digit integers $= 3 	imes 3 	imes 2 	imes 1 = 18$.Case $II$: $3$-digit integers.The first place can be filled by $3$ choices $(1, 2, 3)$. The remaining $2$ places can be filled by the remaining $3$ digits in $3 	imes 2$ ways.Number of $3$-digit integers $= 3 	imes 3 	imes 2 = 18$.Case $III$: $2$-digit integers.The first place can be filled by $3$ choices $(1, 2, 3)$. The second place can be filled by the remaining $3$ digits in $3$ ways.Number of $2$-digit integers $= 3 	imes 3 = 9$.Case $IV$: $1$-digit integers.The possible integers are $1, 2, 3$.Number of $1$-digit integers $= 3$.Total number of distinct positive integers $= 18 + 18 + 9 + 3 = 48$.

The number of distinct positive integers that can be formed using $0, 1, 2, 3$,where each integer is used at most once,is equal to

Similar Questions

How many distinct $9$-digit numbers can be formed by rearranging the digits of the number $223355888$ such that all odd digits occupy even positions?

Find the number of $4$ letter words,with or without meaning,which can be formed out of the letters of the word $ROSE$,where the repetition of the letters is not allowed.

The number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is

The total number of words (with or without meaning) that can be formed out of the letters of the word $'DISTRIBUTION'$ taken four at a time,is equal to...............

The number of natural numbers less than $7,000$ which can be formed by using the digits $0, 1, 3, 7, 9$ (repetition of digits allowed) is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module