Using the principle of inclusionexclusion the number of inte

Using the principle of inclusion-exclusion, the number of integers between 1 and 2000 (inclusive) that are divisible by at least one of 2, 3, 5, 7 is

Using the principle of inclusion-exclusion, the number of integers between 1 and 2000 (inclusive) that are divisible by at least one of 2, 3, 5, 7 is

A = Number of Integers divisible by 2 = 2000/2 = 1000

B = Number of Integers divisible by 3 = 2000/3 = 666

C = Number of integers divisible by 5 = 2000/5 = 400

D = Number of integers divisible by 7 = 2000/7 = 142

A (int) B = 2000/6 = 333

A (int) C = 2000/10 = 200

A (int) D = 2000/14 = 142

B (int) C = 2000/15 = 133

B (int) D = 2000/21 = 95

C (int) D = 2000/35 = 57

A (int) B (int) C = 66

A (int) B (int) D = 47

A (int) C (int) D = 28

B (int) C (int) D = 19

A (int) B (int) C (int) D = 9

Number which are divisible are

=> n(single set) - n(double set) + n(triple set) - n(four sets)

=> 1542

Correct answer is Option B