In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:Choices:- 21/46 1/5 3/25 1/50
Question
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:Choices:- 21/46 1/5 3/25 1/50
Solution
To solve this problem, we need to use the concept of combinations in probability.
Step 1: Find the total number of students in the class. There are 15 boys and 10 girls, so the total number of students is 15 + 10 = 25.
Step 2: Find the total number of ways to select 3 students out of 25. This is a combination problem, which can be solved using the formula nCr = n! / [(n-r)!r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial. So, the total number of ways to select 3 students out of 25 is 25C3 = 25! / [(25-3)!3!] = 2300.
Step 3: Find the number of ways to select 1 girl out of 10 and 2 boys out of 15. This is also a combination problem. The number of ways to select 1 girl out of 10 is 10C1 = 10, and the number of ways to select 2 boys out of 15 is 15C2 = 105. So, the total number of ways to select 1 girl and 2 boys is 10 * 105 = 1050.
Step 4: Find the probability that 1 girl and 2 boys are selected. The probability is the number of favorable outcomes divided by the total number of outcomes. So, the probability that 1 girl and 2 boys are selected is 1050 / 2300 = 21/46.
So, the correct answer is 21/46.
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