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If 16 identical pencils are distributed among 4 children such that each gets at least 3 pencils.The number of ways of distributing the pencils is
- a)15
- b)25
- c)35
- d)40
Correct answer is option 'C'. Can you explain this answer?
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If 16 identical pencils are distributed among 4 children such that eac...
Required number of ways
= coeff. of x16 in (x3 + x4 + x5 + x6 + x7)4
= coeff. of x16 in (x3 + x4 + x5 + x6 + x7)4
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If 16 identical pencils are distributed among 4 children such that eac...
Given: 16 identical pencils, 4 children, each child gets at least 3 pencils.
To find: Number of ways of distributing the pencils.
Solution:
Let's consider the distribution of pencils as balls and children as urns.
Step 1: Distribute 3 pencils to each child.
After giving 3 pencils to each child, we are left with 4 pencils. These 4 pencils can be distributed among 4 children in the following ways:
- All 4 pencils to one child and none to the other 3 children: 4 ways
- 3 pencils to one child and 1 to another child: 4C2 = 6 ways
- 2 pencils to one child and 2 to another child: 4C2 = 6 ways
- 2 pencils to one child and 1 each to the other 2 children: 4C1 × 3C2 = 18 ways
- 1 pencil to each of the 4 children: 1 way
Total number of ways of distributing the 4 pencils = 4 + 6 + 6 + 18 + 1 = 35
Therefore, the total number of ways of distributing 16 identical pencils among 4 children such that each child gets at least 3 pencils is 35.
Answer: (c) 35
To find: Number of ways of distributing the pencils.
Solution:
Let's consider the distribution of pencils as balls and children as urns.
Step 1: Distribute 3 pencils to each child.
After giving 3 pencils to each child, we are left with 4 pencils. These 4 pencils can be distributed among 4 children in the following ways:
- All 4 pencils to one child and none to the other 3 children: 4 ways
- 3 pencils to one child and 1 to another child: 4C2 = 6 ways
- 2 pencils to one child and 2 to another child: 4C2 = 6 ways
- 2 pencils to one child and 1 each to the other 2 children: 4C1 × 3C2 = 18 ways
- 1 pencil to each of the 4 children: 1 way
Total number of ways of distributing the 4 pencils = 4 + 6 + 6 + 18 + 1 = 35
Therefore, the total number of ways of distributing 16 identical pencils among 4 children such that each child gets at least 3 pencils is 35.
Answer: (c) 35
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If 16 identical pencils are distributed among 4 children such that eac...
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If 16 identical pencils are distributed among 4 children such that each gets at least 3 pencils.The number of ways of distributing the pencils isa)15b)25c)35d)40Correct answer is option 'C'. Can you explain this answer?
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