Binomial Theorem

Find the 8th term of the expansion of (1/2x-y)^10

-15x^3y^7

Find the seventh term of the expansion of (-3p-2q)^11

-7,185,024 p^5 q^6

Find the 6th term of the expansion of (2p - 3q)^11.

-7,185,024 p^6q^5

Find the 5th term of the expansion of (x + y)^9.

126x^5y^4

Find the seventh term of the expansion of (3x+7y)^11

13207982634x^5y^6

Find the 7th term of the expansion of (3p + 2q)^9.

145,152p^3q^6

Write an expression to represent the sum of the numbers in the nth row of Pascal's triangle.

2^N

How many different ways are there to form groups of 4 in Mrs. Meinert's class given there are 32 students to begin with?

35,960

Rafael is taking a test that contains a section of 12 true-false questions. How many of the possible groups of answers to these questions have exactly 8 correct answers of false?

495

Rafael is racing in the 100 meter dash at the CIF finals track meet. He hopes to be in the top 3. How many different ways are there for the race to turn out if we only care about 1st, 2nd, and 3rd given there are 9 people in the race?

504