A five-digit number divisible by 3 has to be | 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 sum of all given digits is $0+1+2+3+4+5 = 15$. Since we need to form

Vedclass · Accepted Answer

$216$

Vedclass · Answer

(A) number is divisible by $3$ if the sum of its digits is divisible by $3$. The sum of all given digits is $0+1+2+3+4+5 = 15$. Since we need to form a $5$-digit number,we must exclude one digit such that the sum of the remaining $5$ digits is divisible by $3$.Case $1$: Exclude $0$. The remaining digits are ${1, 2, 3, 4, 5}$. The sum is $15$,which is divisible by $3$. The number of ways to arrange these $5$ digits is $5! = 120$.Case $2$: Exclude $3$. The remaining digits are ${0, 1, 2, 4, 5}$. The sum is $12$,which is divisible by $3$. The number of $5$-digit numbers that can be formed is $5! - 4! = 120 - 24 = 96$ (subtracting cases where $0$ is in the first position).Total ways = $120 + 96 = 216$.

$A$ five-digit number divisible by $3$ has to be formed using the numerals $0, 1, 2, 3, 4,$ and $5$ without repetition. The total number of ways in which this can be done is

Similar Questions

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

The value of $r$ for which $^{20}C_r \cdot ^{20}C_0 + ^{20}C_{r-1} \cdot ^{20}C_1 + ^{20}C_{r-2} \cdot ^{20}C_2 + \dots + ^{20}C_0 \cdot ^{20}C_r$ is maximum is:

In how many different ways can the letters of the word '$JUDGE$' be arranged in such a way that the vowels always come together?

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module