Question

A scientist needs to take acid rain samples from 5 lakes in the country, and there are a total of 11 lakes. How many different sets of samples are possible?

A) 11
B) 5
C) 55
D) 462

Answer 1

To determine the number of different sets of acid rain samples from 5 out of 11 lakes, the combination formula is used, which results in 462 different sets of samples possible.

Step-by-step explanation:

To calculate the number of different sets of samples possible when taking acid rain samples from 5 lakes out of 11, we need to use the combination formula. The formula for combinations is given by C(n, k) = n!/(k!*(n-k)!), where n is the total number of items, here 11 lakes, and k is the number of items to choose, in this case 5 lakes.

The calculation proceeds as follows:

1. Factorial calculation for 11 (11! = 11*10*9*8*7*6*5*4*3*2*1).
2. Factorial calculation for 5 (5! = 5*4*3*2*1).
3. Subtract 5 from 11 (11-5 = 6) and calculate the factorial for 6 (6! = 6*5*4*3*2*1).
4. Divide 11! by the product of 5! and 6! (11! / (5!*6!)).
5. Combinations calculation gives us the result.

After performing these calculations, we find that the total number of different sets of samples possible is 462 (C(11, 5) = 462).

Therefore, the correct answer is D) 462.