A lady gives a dinner party for six guests. In how many ways they be selected from among 10 friends
Question
A lady gives a dinner party for six guests. In how many ways they be selected from among 10 friends
Solution
The problem can be solved using the concept of combinations in mathematics.
A combination is a selection of items without considering the order. In this case, the lady is selecting 6 guests out of 10 friends, and the order in which they are selected does not matter.
The formula for combinations is:
C(n, r) = n! / [(n-r)! * r!]
where:
- n is the total number of items,
- r is the number of items to select,
- "!" denotes factorial, which is the product of all positive integers up to that number.
Substituting the given values into the formula:
C(10, 6) = 10! / [(10-6)! * 6!]
= 10987654321 / [(4321) * (65432*1)]
After simplifying, we find that the lady can select 6 guests out of 10 friends in 210 different ways.
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