The number of integers between 2,000 and 5,00 | vedclass

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

Question

(A) number is divisible by $3$ if the sum of its digits is divisible by $3$.The thousands place can be filled with $2, 3,$ or $4$ because the number m

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) number is divisible by $3$ if the sum of its digits is divisible by $3$.The thousands place can be filled with $2, 3,$ or $4$ because the number must be between $2,000$ and $5,000$.Case $1$: Thousands place is $2$.Possible sets of remaining $3$ digits from ${0, 1, 3, 4}$ such that the sum is divisible by $3$:- ${0, 1, 3}$ (sum $= 2+0+1+3 = 6$)- ${0, 3, 4}$ (sum $= 2+0+3+4 = 9$)Each set can be arranged in $3! = 6$ ways. Total $= 2 	imes 6 = 12$.Case $2$: Thousands place is $3$.Possible sets of remaining $3$ digits from ${0, 1, 2, 4}$ such that the sum is divisible by $3$:- ${0, 1, 2}$ (sum $= 3+0+1+2 = 6$)- ${0, 2, 4}$ (sum $= 3+0+2+4 = 9$)Each set can be arranged in $3! = 6$ ways. Total $= 2 	imes 6 = 12$.Case $3$: Thousands place is $4$.Possible sets of remaining $3$ digits from ${0, 1, 2, 3}$ such that the sum is divisible by $3$:- ${0, 2, 1}$ (sum $= 4+0+2+1 = 7$ - No)- ${0, 2, 3}$ (sum $= 4+0+2+3 = 9$)- ${1, 2, 3}$ (sum $= 4+1+2+3 = 10$ - No)Only ${0, 2, 3}$ works. Total $= 1 	imes 6 = 6$.Total numbers $= 12 + 12 + 6 = 30$.

The number of integers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) such that the number is a multiple of $3$ is:

Similar Questions

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

Find $r$ if $^{5}P_{r} = 2 \times ^{6}P_{r-1}$.

In how many ways can the letters of the word $GARDEN$ be arranged such that the vowels appear in alphabetical order?

There are $9$ chairs in a room,and $6$ people are to be seated. One of these chairs is a special chair reserved for a special guest. In how many ways can these people be seated?

If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module