In how many ways can 2 out of 5 different fruits be selected?

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Q: In how many ways can 2 out of 5 different fruits be selected?

Solution: The number of ways to choose 2 fruits from 5 is C(5, 2) = 10.

Steps: 13

Step 1: Understand that we have 5 different fruits.
Step 2: We want to select 2 fruits from these 5.
Step 3: The formula to find the number of ways to choose 'r' items from 'n' items is called 'combinations' and is written as C(n, r).
Step 4: In our case, n = 5 (the total number of fruits) and r = 2 (the number of fruits we want to select).
Step 5: The formula for combinations is C(n, r) = n! / (r! * (n - r)!).
Step 6: Calculate C(5, 2) using the formula: C(5, 2) = 5! / (2! * (5 - 2)!).
Step 7: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 8: Calculate 2! = 2 × 1 = 2.
Step 9: Calculate (5 - 2)! = 3! = 3 × 2 × 1 = 6.
Step 10: Now plug these values into the formula: C(5, 2) = 120 / (2 * 6).
Step 11: Calculate the denominator: 2 * 6 = 12.
Step 12: Now divide: 120 / 12 = 10.
Step 13: Therefore, there are 10 different ways to select 2 fruits from 5.