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Bunuel
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SN_09
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Bunuel
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SN_09
In how many ways can 5 identical apples be put into 3 different bowls such that at least 1 apple is included in each bowl?

A. 6
B. 10
C. 142
D. 150
E. 243

Hi Bunuel,

Can we please have the official explanation posted here? Just want to verify the method I have used to arrive at the answer.

Thank you!

An official solution isn't available, but here's how I would approach the problem:

Since each bowl must contain at least one apple, we can start by distributing 3 apples as {1 - 1 - 1}, leaving 2 apples to be allocated.

When distributing the 2 remaining apples one at a time, there are 3 possible ways: {0 - 1 - 1}, {1 - 0 - 1}, or {1 - 1 - 0}.

When placing both remaining apples to a single bowl, there are also 3 possible ways: {2 - 0 - 0}, {0 - 2 - 0}, or {0 - 0 - 2}.

Therefore, there are a total of 3 + 3 = 6 ways.

Answer: A.
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Perfect, this is helpful. Thanks a ton!


Bunuel
SN_09
In how many ways can 5 identical apples be put into 3 different bowls such that at least 1 apple is included in each bowl?

A. 6
B. 10
C. 142
D. 150
E. 243

Hi Bunuel,

Can we please have the official explanation posted here? Just want to verify the method I have used to arrive at the answer.

Thank you!

An official solution isn't available, but here's how I would approach the problem:

Since each bowl must contain at least one apple, we can start by distributing 3 apples as {1 - 1 - 1}, leaving 2 apples to be allocated.

When distributing the 2 remaining apples one at a time, there are 3 possible ways: {0 - 1 - 1}, {1 - 0 - 1}, or {1 - 1 - 0}.

When placing both remaining apples to a single bowl, there are also 3 possible ways: {2 - 0 - 0}, {0 - 2 - 0}, or {0 - 0 - 2}.

Therefore, there are a total of 3 + 3 = 6 ways.

Answer: A.
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