Find the value of the factorial 3 Type the whole number Fi

Find the value of the factorial 3! = _____     (Type the whole number)

Fin the value of the permutation. 3P3 = _____   (Type the whole number)

Find the value of the combination 4C4 = _______   (Type the whole number)

Outside a home, there is a 9-key keypad numbered 1 through 9. The correct three-digit code will open the garage door. The numbers can be repeated in the code.

How many codes are possible? ________ (Type an integer or fraction. Simplify your answer)

The probability that the correct code is given on the first try, assuming that the owner doesn’t remember it is _____ (Type an integer or fraction. Simplify your answer)

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of seven students and eight faculty.

What is the probability of selecting a jury of all students?

What is the probability of selecting a jury of all faculty?

What is the probability of selecting a jury of 3 students and 2 faculty?

Solution

A)

Find the value of the factorial 3! = 3*2*1 = 6

Fin the value of the permutation. 3P3 = 3! / (3-3)! = 3! /(0!) = 3! = 6

Find the value of the combination 4C4 = 4! / ( 4! * 0! ) = 1

B)

Outside a home, there is a 9-key keypad numbered 1 through 9. The correct three-digit code will open the garage door. The numbers can be repeated in the code.! =

Solution:

How many codes are possible? ________ (Type an integer or fraction. Simplify your answer)

Each of the three blank spaces can take 9 values. Therefore total number of values = 9*9*9 = 729 ways

The probability that the correct code is given on the first try, assuming that the owner doesn’t remember it is _____ (Type an integer or fraction. Simplify your answer)

Only one of the 729 codes is correct. Thus, probability of getting it correct on first try = 1 / 729

C)

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of seven students and eight faculty.

Solution:

Number of ways of selecting five people from 15 = 15 C 5 = 3003 ways

What is the probability of selecting a jury of all students?

= 7 C 5 / 15 C 5

= 21 / 3003

= 1 / 43

What is the probability of selecting a jury of all faculty?

= 8 C 5 / 15 C #

= 56 / 3003

= 8 / 429

What is the probability of selecting a jury of 3 students and 2 faculty?

= (7 C 3 ) * (8 C 2) / 15 C 5

= 980 / 3003

= 140 / 429

Hope this helps. Ask if you have any doubts.