4. The first 100 natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, ..., 97, 98, 99, 100 You must choose 99 numbers from these 100 numbers such that the sum of the selected 99 numbers is a multiple of 7. The total number of such possible selections is .
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14
Step-by-step explanation:
The sum of first 100 numbers is 5050.
A group of 99 numbers need to be selected from the 100 numbers, i.e, one number has to be omitted from the 100 numbers such that the sum of the 99 numbers should be a multiple of 7.
Omitting the following numbers will lead to forming groups of 99 numbers whose sum will be a multiple of seven. the numbers are 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94. Hence 14 such selections are possible whose sum will be a multiple of 7
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