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3 years ago

give 12 consecutive integers, in how many ways can three of these integers be selected to give a sum which divides by 4?

Mathematics

1 answer:

BaLLatris [955]3 years ago

7 0

Answer:

55 ways

Step-by-step explanation:

Out of 12 consecutive integers:

3 - divide by 4, so the remainder is 0
3- give remainder of 1
3- give remainder of 2
3 - give remainder of 3

Sum of 3 integers will be divisible by 4 if the remainders are:

0 - 0 - 0 ⇒ 1 combination
0 - 1 - 3 ⇒ 3*3 = 9 combinations
0 - 3 - 1 ⇒ 3*3 = 9 combinations
1 - 1 - 2 ⇒ 2*3 = 6 combinations
1 - 2 - 1 ⇒ 2*3 = 6 combinations
2 - 1 - 1 ⇒ 2*3 = 6 combinations
3 - 0 - 1 ⇒ 3*3 = 9 combinations
3 - 1 - 0 ⇒ 3*3 = 9 combinations

So total number of combinations is:

1 + 4*9 + 3*6 = 55

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