Help me solve these! Give the expression of ways to distribute 15 distinguishabl

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Help me solve these!

Give the expression of ways to distribute 15 distinguishable balls into five distinguishable boxes so that the boxes have one, two, three, four, and five balls in them, respectively. Assume there is no restriction on which box gets one ball, which box gets two balls, etc. Solve the recurrence an = an-1 + an-2, with a0 = 2 and a1 = 1 (This is called the Lucas sequence, and is closely related to the Fibonacci sequence). Solve the recurrence an = 12an-1 - 35an-2, ao = -3, and a1 = 1. Let Fi denote the ith element of the Fibonacci sequence. Prove that F1 + F3 + F5 + + F2n-1 = F2n. Prove that F3n is even. (Hint: you can use mathematical induction to prove the above two claims.)

Explanation / Answer

Question 8)

(5C1 X 15C1)X(4C1 X 14C2)X(3C1 X 12C3)X(2C1 X 9C4)X(1C1 X 5C5)

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