Permutations, combinations and polynomials module exam

Question 1.

How many ways can the word banana be rearranged so that all the a’s are together.

Question 2.

Solve for n

ⁿ⁺¹P₄ = 32760

Question 3.

Solve for n

ⁿC₄ =5 ⁿC₃

Question 4.

Expand (4x – 1/(x))^5

Question 5.

A group of 15 people are waiting to enter a dinner, 4 are chosen at random, if they are then seated around a circular table. How many combinations of this situation are there?

Question 6.

Two successive numbers, 715 and 1287, are found in the nth row of a pascal triangle. Determine the n value.

Question 7.

Without expanding, what is the 6th term of (3x – 2y)^9

Answer.

Question 1.

Question 2.

n=14

Question 4.

Question 5.

Question 6.

n=13