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

Step-by-step 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)

= $10_P_4$

= $\frac{10!}{(10-4)!}$

=  $\frac{10!}{6!}$

= $\frac{10\times 9\times 8\times 7\times 6!}{6!}$

= 10 × 9 × 8 × 7

= 5040

2) Here the total number of machine = 11

The different combinations of machines can Geoff choose from to use

= $11_C_3$

= $\frac{11!}{(11-3)!3!}$

= $\frac{11!}{8!3!}$

= $\frac{11\times 10\times 9\times 8!}{8!\times 6}$

= 11 × 5 × 3

= 165