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The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is
- a)406
- b)130
- c)142
- d)136
Correct answer is option 'D'. Can you explain this answer?
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The number of ways in which 21 identical apples can be distributed amo...
After giving 2 apples to each child 15 apples left now 15 apples can be distributed in 15+3-1C2 = 17C2 ways
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The number of ways in which 21 identical apples can be distributed amo...
Approach:
To solve this problem, we can use a combinatorial approach by distributing the apples among the children while ensuring that each child receives at least 2 apples.
Step 1: Minimum Distribution of Apples
Since each child must receive at least 2 apples, we distribute 2 apples to each child initially. This leaves us with 15 apples to distribute among the children.
Step 2: Distributing the Remaining Apples
We can consider the problem as distributing 15 identical apples among 3 children without any restrictions. This is equivalent to finding the number of ways to place 2 dividers among 15 apples, representing the distribution among the 3 children.
Step 3: Applying Combination Formula
Using the combination formula, the number of ways to distribute 15 identical apples among 3 children is given by C(15+3-1, 3-1) = C(17, 2) = 136.
Therefore, the number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples is 136. Hence, the correct answer is option 'D'.
To solve this problem, we can use a combinatorial approach by distributing the apples among the children while ensuring that each child receives at least 2 apples.
Step 1: Minimum Distribution of Apples
Since each child must receive at least 2 apples, we distribute 2 apples to each child initially. This leaves us with 15 apples to distribute among the children.
Step 2: Distributing the Remaining Apples
We can consider the problem as distributing 15 identical apples among 3 children without any restrictions. This is equivalent to finding the number of ways to place 2 dividers among 15 apples, representing the distribution among the 3 children.
Step 3: Applying Combination Formula
Using the combination formula, the number of ways to distribute 15 identical apples among 3 children is given by C(15+3-1, 3-1) = C(17, 2) = 136.
Therefore, the number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples is 136. Hence, the correct answer is option 'D'.
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The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, isa)406b)130c)142d)136Correct answer is option 'D'. Can you explain this answer?
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