Here's the solution and answers to the ME board questions in Mathematics (Statistics and Probability)

1. In how many ways can you arrange a group of 5 girls and 3 boys in 7 vacant chairs?

Solution:

The total number of persons to be seated is 8 and the number of chairs is only 7.

When words denoting “arrangement” are used, it most likely pertains to permutations.

So, the formula to be used is permutation of 8 taking 7 at a time.

n = 8, r = 7, nPr, then use your calculator or this formula

nPr = n!/(n-r)! = 8!(8-1)!=40320 permutations or arrangements

2. How many 3-digit numbers can you make out of the numbers 1 to 5 without repetition?

Solution:

Since the number varies as you rearrange the digits (example 1342 is different from 1423), then this problem is about permutation.

So, the formula is the permutation of 5 numbers taken 3 at a time.

n = 5, r = 3, nPr; use your calculator or this formula: nPr = n!/(n-r)!

nPr = 5!/(5-3)!=60 permutations

3. There are 2 white, 3 red, …

1. In how many ways can you arrange a group of 5 girls and 3 boys in 7 vacant chairs?

Solution:

The total number of persons to be seated is 8 and the number of chairs is only 7.

When words denoting “arrangement” are used, it most likely pertains to permutations.

So, the formula to be used is permutation of 8 taking 7 at a time.

n = 8, r = 7, nPr, then use your calculator or this formula

nPr = n!/(n-r)! = 8!(8-1)!=40320 permutations or arrangements

**A. 40320**2. How many 3-digit numbers can you make out of the numbers 1 to 5 without repetition?

Solution:

Since the number varies as you rearrange the digits (example 1342 is different from 1423), then this problem is about permutation.

So, the formula is the permutation of 5 numbers taken 3 at a time.

n = 5, r = 3, nPr; use your calculator or this formula: nPr = n!/(n-r)!

nPr = 5!/(5-3)!=60 permutations

**C. 60**3. There are 2 white, 3 red, …