Question

three magazines? How many permutations of the letters of the word OUTSIDE have consonants in the first and last place? Compute: a) 9C4 b) 8P3

Answer 1

Q1

• CThere are 3 consonants.
• 1st place can be filled in 3 ways and then last place can be filled in 2 ways
• Rest of the 5 letters can be filled in 5! or 5 factorial ways
• So totally, we will have 6 x 5 factorial or we can say 6 factorial ways to write the letters of the word OUTSIDE in which 1st and last letters will be consonants
• So that comes to 6 x 5 x 4 x 3 x 2 x 1 = 720 ways

Q2

Part a)

9 x 8 x 7 x 6 1 x 2 x 3 x 4 4 +

9C4 = 126

Part b)

8! 8P3 = 18 - 3)!

8P3

8 x 7 x 6 x 5! 8P3 = -

8P3 = 8 x 7 x 6

8P3 = 336