# The total numbers of number, 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________ Option: 1 36 Option: 2 32 Option: 3 34 Option: 4 24

We need three digits numbers.

Since 1 + 2 + 3 + 4 + 5 = 15

Numbers divisible by 3 are (1,3,5), (1,2,3), (2,3,4) and (3,4,5)

Total permutation is $4\times3!=24$

Numbers divisible by 5 are (x,x,5)

Total permutation is $4\times3\times1=12$

Numbers divisible by both 3 and 5 are (1,3,5) and (3,4,5)

Total permutation is $2\times2\times1=4$

Hence required permutation is $24+12-4=32$

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