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Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are not divisible by 2, 3 and 5.

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Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are not divisible by 2, 3 and 5.

(a) 22

(b) 25

(c) 26

(d) 33

I got this question in unit test.

My question is taken from Number Theory in portion Number Theory of Data Structures & Algorithms II

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The correct choice is (c) 26

Easiest explanation - Consider sample space S={1,…100}. Consider three subsets A, B, C that have elements that are divisible by 2, 3, 5 respectively. Find integers that are divisible by A and B, B and C, A and C. Then find the integers that are divisible by A, B, C. Applying the inclusion-exclusion principle, 100 − (50 + 33 + 20) + (16 + 10 + 6) − 3 = 26.

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