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

3. How many permutations are there for the letters in the word LOLLIPOP?

1680

6720

10,080

40,320

4. What is the fourth term in the expansion of (x + 2y)8?

336x5y3

448x5y3

1120x4y4

1680x4y4

### Best Answer

3) 8!/3!2!2! = 1680

4) 8C3x⁵(2y)³ => 56x⁵(8)y³

=> 448x⁵y³

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### Answers

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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