In a group of 54 candidates, 16 are female and the remaining are male. If four are to be randomly selected, what is the probability that there will be only female candidates selected?
If the the girls are not being replaced (i.e put back in the lot) it would be (16/54)+(15/53)+(14/52)+(13/51) since you're not replacing them, the amount of people inside the group decreases.
Now fi the candidates were being replaced, the amount of candidates in total would not change, making it (16/54)*4
I kept getting the question wrong because I assumed they were being replaced. Thank you!
To find the probability of selecting only female candidates, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the number of ways to select four candidates from a group of 54, which is denoted as 54C4 (read as "54 choose 4").
The number of favorable outcomes is the number of ways to select four female candidates from a group of 16 females, which is denoted as 16C4.
The probability of selecting only female candidates can then be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Let's calculate the probability step by step:
1. Calculate 54C4:
- Use the formula: nCr = n! / [(n-r)! * r!], where n is the total number of candidates and r is the number of candidates to be selected.
- Plug in the values: n = 54 and r = 4.
- Calculate: 54C4 = 54! / [(54-4)! * 4!]
2. Calculate 16C4:
- Use the formula: nCr = n! / [(n-r)! * r!], where n is the total number of female candidates and r is the number of female candidates to be selected.
- Plug in the values: n = 16 and r = 4.
- Calculate: 16C4 = 16! / [(16-4)! * 4!]
3. Calculate the probability:
- Divide the number of favorable outcomes (16C4) by the total number of possible outcomes (54C4).
- Probability = 16C4 / 54C4
By following these steps, you can find the probability that there will be only female candidates selected.