Ajay has a bag of chocolates with 4 dark chocolates and 7 white chocolates. In how many ways can he pick the chocolates so that he picks exactly 4 white chocolates?
Question
Ajay has a bag of chocolates with 4 dark chocolates and 7 white chocolates. In how many ways can he pick the chocolates so that he picks exactly 4 white chocolates?
Solution
The problem can be solved using the concept of combinations in probability.
The total number of white chocolates is 7 and Ajay needs to pick exactly 4.
The number of ways to pick 4 white chocolates out of 7 is given by the combination formula:
C(n, r) = n! / [(n-r)! * r!]
where:
- n is the total number of items,
- r is the number of items to choose,
- "!" denotes factorial, which is the product of all positive integers up to that number.
So, substituting the given values:
C(7, 4) = 7! / [(7-4)! * 4!]
= (7654321) / [(321) * (432*1)]
= (765) / (432)
= 35
So, Ajay can pick exactly 4 white chocolates from the bag in 35 different ways.
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