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Veseljchak [2.6K]
3 years ago
7

How can you divide 133 nickels into 8 bags so that there are the same number of nickels in each bag and the number in each bag i

s odd and there are none left over?
Mathematics
1 answer:
MaRussiya [10]3 years ago
3 0
There is no way to divide them because 133 is odd, so 133 divided by 8 would be 16.625.
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Use the principle of inclusion and exclusion to find the number of positive integers less than 1,000,000 that are not divisable
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This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
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Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.

∴N(c₁) = \frac{999,999}{6} = 166666
N(c₂) = \frac{999,999}{4} = 250000
∴N(c₁c₂) = \frac{999,999}{24} = 41667
∴ Number of positive integers that are not divisible by 4 or 6,

N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
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