Question

30 pts + BRAINLIEST

Answer 1

Answer:

Number of permutations = 5040

Step-by-step explanation:

We are given the word 'INNOVATIVE', that has total 10 letters.

Now, we are asked to form words using exactly 4 letters at a time i.e. out of 10 letters we are using 4.

Therefore, the number of permutations that can be formed using 4 letters are = P(10,4)

i.e. $10_{P_{4} }$

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

= $\frac{10!}{6!}$

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

= 10*9*8*7

= 5040

Answer 2

Answer: 5040

Step-by-step explanation:

npr = n! / (n - r)!

numbers of letters given = 10

permutation that can be formed using 4 letters at a time= 10 P ₄

=10! / (10 - 4)! = 10! / 6!

= 10 ×9 ×8×7 ×6! /6! ( the 6! will cancel out)

= 10×9 ×8×7=5040

Therefore, the number of permutations are 5040