# Probability - Check

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Could someone check these answers for me. Thanks
1. (3x+y)^7 =
2187x^7 + 5103x^6y + 5103x^5y^2 + 8505x^4y^3 + 2835x^3y^4 + 567x^2y^5 + 63xy^6 + y^7

2. Eight people are boarding an airplane. Two have tickets for first class and board before those in the economy class. In how many ways can the 8 board?

3. Find the number of distinguishable permutations of these group of letters: I,N,T,E,G,R,A,T,E

4. From a pool of 7 juniors and 11 seniors, 4 captains must be chosen for teams. How many different combination are possible if 2 juniors and 2 seniors are picked?

5. A child returns a five-volume set of books to a shelf. What is the probability that the books are shelved in the correct order?

6. A six sided dice is rolled six times. What is the probability that each side is rolled exactly once?

• Probability - (#6 of 6) -

6. 1/6^6 is the correct answer, for each numbered side. 1/6^5 is the probability that SOME number will appear six times in a row.

• Probability - Check -

Thanks for the help!