I have six identical oranges and six distinct apples. In how many ways can I have a basket of five fruits containing at least one apple and at least one orange .
please solve it fast guys its urgent
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Answers
The number of ways in which 10 identical apples can be distributed among 6 children so that each child receives at least one apple is?
My Attempt:
I got the number possibilities to be: (1,1,1,1,1,5),(1,1,1,1,2,4),(1,1,2,2,2,2),(1,1,1,2,2,3)(1,1,1,1,1,5),(1,1,1,1,2,4),(1,1,2,2,2,2),(1,1,1,2,2,3)
Since they are identical apples, the number of ways each of these possibilities can be formed is 1.
Therefore the number of ways in which a basket of 5 fruits containing at least 1 apple and at least 1 orange can be picked is 14 ways.
Given:
Number of identical oranges = 6
Number of distinct apples = 6
Number of fruits that a basket can contain = 5
To Find:
Number ways in which a basket of 5 fruits containing at least 1 apple and at least 1 orange can be picked.
Solution:
The given question can be solved as shown below.
Given that,
Number of identical oranges = 6
Number of distinct apples = 6
Number of fruits that a basket can contain = 5
As 6 oranges are identical it can be considered as 1 unit.
Now total number of ways of picking 5 fruits = ⁷C₅ = ( 7 × 6 )/2 = 21 ways
Number of ways of picking all the oranges = 1 way ( Oranges are identical )
Number of ways of picking all the apples = ⁶C₅ = 6 ways
Now the number of ways in which at least one orange and at least one apple could be picked = Total number of ways to pick 5 fruits - ( Number of ways of picking all oranges + Number of ways of picking all apples )
⇒ Now the number of ways in which at least one orange and at least one apple could be picked = 21 - ( 1 + 6 ) = 21 - 7 = 14 ways
Therefore the number of ways in which a basket of 5 fruits containing at least 1 apple and at least 1 orange can be picked is 14 ways.
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