The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1,2,3,4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is

Question

The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1,2,3,4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We need three digits numbers. Since 1+2+3+4+5=15 So, number of possible triplets for multiple of 15 is 1 × 2 × 2 so Ans. =4 × 3+4 × 3-1 × 2 × 2=32

Q. The total number of numbers, lying between $100$ and $1000$ that can be formed with the digits $1, 2, 3, 4, 5,$ if the repetition of digits is not allowed and numbers are divisible by either $3$ or $5,$ is____

We need three digits numbers.
Since $1 + 2 + 3 + 4 + 5 = 15$
So, number of possible triplets for multiple of $15$ is $1 \times 2 \times 2$
so Ans. $= 4 \times 3 + 4 \times 3 - 1 \times 2 \times 2 = 32$

Q. The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1,2,3,4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is____

We need three digits numbers. Since 1+2+3+4+5=15 So, number of possible triplets for multiple of 15 is 1×2×2 so Ans. =4×3+4×3−1×2×2=32

Q. The total number of numbers, lying between $100$ and $1000$ that can be formed with the digits $1, 2, 3, 4, 5,$ if the repetition of digits is not allowed and numbers are divisible by either $3$ or $5,$ is____

We need three digits numbers.
Since $1 + 2 + 3 + 4 + 5 = 15$
So, number of possible triplets for multiple of $15$ is $1 \times 2 \times 2$
so Ans. $= 4 \times 3 + 4 \times 3 - 1 \times 2 \times 2 = 32$