Question

Using the letters in the word INNOVATIVE, find the number of permutations that can be formed using 4 letters at a time. Show your work or explain how you got your answer.

The gym has 11 different types of machines in the weight room. Geoff has time to use only 3 of them this afternoon. How many different combinations of machines can Geoff choose from to use? Show your work or explain how you got your answer

Answer 1

Answer: 1) 5040 and 2) 165

Explanation:

1) Here total number of letters = 10

The number of permutations that can be formed using 4 letters at a time

= P (10, 4)

=
`10_P_4`

=
`(10!)/((10-4)!)`

=
`(10!)/(6!)`

=
`(10* 9* 8* 7* 6!)/(6!)`

= 10 × 9 × 8 × 7

= 5040

2) Here the total number of machine = 11

The different combinations of machines can Geoff choose from to use

=
`11_C_3`

=
`(11!)/((11-3)!3!)`

=
`(11!)/(8!3!)`

=
`(11* 10* 9* 8!)/(8!* 6)`

= 11 × 5 × 3

= 165