### How many permutations are there of the word LOLLIPOP?

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1#

Rearrange letters so as to group duplicates together:

I LLL OO PP

1 I

3 L's

2 O's

2 P's

8 letters in total

Permutations: 8! / (1! * 3! * 2! * 2!) = 1680

4.

(x + 2y)^8 = ∑ [k = 0 to 8] C(8,3) x^(8−k) (2y)^k

Since we start with k = 0, then 4th terms means k = 3

C(8,3) x^(8−3) (2y)^3

= 56 x^5 * 8y^3

= 448 x^5 y^3

Rearrange letters so as to group duplicates together:

I LLL OO PP

1 I

3 L's

2 O's

2 P's

8 letters in total

Permutations: 8! / (1! * 3! * 2! * 2!) = 1680

4.

(x + 2y)^8 = ∑ [k = 0 to 8] C(8,3) x^(8−k) (2y)^k

Since we start with k = 0, then 4th terms means k = 3

C(8,3) x^(8−3) (2y)^3

= 56 x^5 * 8y^3

= 448 x^5 y^3

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