2 years ago

3. How many permutations are there for the letters in the word LOLLIPOP? 1680 6720 10,080 40,3204. What is the fourth term in the expansion of (x + 2y)8? 336x5y3 448x5y3 1120x4y4 1680x4y4

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

Best Answer

4) 8C3x⁵(2y)³ => 56x⁵(8)y³

=> 448x⁵y³

:)>

Other 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

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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