Question

suppose we want to choose three objects, without replacement from the four objects pencil, eraser, desk, and chair. a) how many ways can this be done, if the order of the choices matters?b) how many ways can this be done, if the order of the choices does not matter?

Answer 1

suppose we want to choose three objects, without replacement from the four objects pencil, eraser, desk, and chair.





a) how many ways can this be done, if the order of the choices matters?





b) how many ways can this be done, if the order of the choices does not matter?

Part a)

Find out the permutation

Applying the formula

P=n!/[n-r]!

where

n=4

r=3

substitute

P=4!/[4-3]!

P=24

answer part a is 24 ways

Part b

Find out the combination

Applying the formula

C=n!/[(n-r)!*r!]

where

n=4

r=3

substitute

C=4!/[(4-3)!*3!]

C=4

answer part b is 4 ways