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A botanical garden has 7 distinct types of flowers. In how many ways can a gardener select 3 different types to create a visually appealing bouquet?
To solve this problem, we need to calculate the number of ways to choose 3 types of flowers from 7 distinct types.
The number of combinations is given by the combination formula:
A card game uses a deck of 52 cards. How many ways can a player draw 5 cards such that exactly 3 of them are aces?
To solve this problem, we need to find the number of ways to choose exactly 3 aces and 2 non-ace cards from a standard deck of 52 cards.
The number of ways to choose 3 aces from 4 is:
Choosing 2 non-ace cards from the remaining 48:
The number of ways to choose 2 cards from 48 non-aces is:
A team of 5 members is to be formed from a group of 10 candidates. How many different teams can be formed if 2 specific candidates must always be included?
Since 2 specific candidates must always be included, we only need to choose the remaining 3 members from the other 8 candidates.