A box contains 3 red balls and 2 blue balls. In how many ways can 2 balls be sel
Practice Questions
Q1
A box contains 3 red balls and 2 blue balls. In how many ways can 2 balls be selected from the box?
10
6
5
3
Questions & Step-by-Step Solutions
A box contains 3 red balls and 2 blue balls. In how many ways can 2 balls be selected from the box?
Step 1: Count the total number of balls in the box. There are 3 red balls and 2 blue balls, so 3 + 2 = 5 balls in total.
Step 2: We need to find out how many ways we can choose 2 balls from these 5 balls.
Step 3: Use the combination formula, which is written as nCr, where n is the total number of items (balls) and r is the number of items to choose. Here, n = 5 and r = 2.
Step 4: The combination formula is nCr = n! / (r! * (n - r)!). For our case, it becomes 5C2 = 5! / (2! * (5 - 2)!).
Step 5: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120), 2! (which is 2 x 1 = 2), and (5 - 2)! (which is 3! = 3 x 2 x 1 = 6).
Step 6: Substitute these values into the formula: 5C2 = 120 / (2 * 6).
Step 7: Calculate the denominator: 2 * 6 = 12.
Step 8: Now divide: 120 / 12 = 10.
Step 9: Therefore, there are 10 different ways to select 2 balls from the box.
Combinatorics – The problem tests the understanding of combinations, specifically how to calculate the number of ways to choose a subset from a larger set without regard to the order of selection.
