please answer all of the questions they have to do with the binomial theorem.

1)From a class of 20 girls and 14 boys a group of 5 students must be selected to act as guides for the annual open house tours given to grade 8 students. How many different selections of 5 guides can be made ifno boys are chosen?

2)How many combinations can be formed from the letters of the word HELP taking two at a time?

3)There are 26 red cards and 26 black cards in a standard deck of 52 cards. The red cards are divided into two suits (hearts and diamonds) and the black cards are divided into two suits (clubs and spades). The 13 cards within each suit are known as the 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, king, queen, and ace of that particular suit. In the game of 5-card poker, each player is dealt 5 cards. How many 5-card hands can be dealt such thatthere are onlyhearts?

4)A box contains 4 red marbles, 3 blue marbles, and 5 yellow marbles. In how many ways can one select a set of 5 marbles from the box such that2 are red and 3 are blue?

5)Using letters from the word MANUSCRIPT, how many 4-letter arrangements consisting of 3 different consonants and 1 vowel can be formed if no letter is repeated?

6)If you have one of each of a penny, nickel, dime, quarter, looney, and tooney, how many different amounts can you leave as a tip for a waiter if you leave at least one coin? (Hint: Use cases.

7)How many 10-card hands can be dealt from a standard deck of 52 cards that consist ofno clubs?

8)From a class of 9 boys and 10 girls a committee of 3 boys and 3 girls is to be chosen. In how many ways can this be done ifAllan must be on the committee but Lindsey must not be on the committee?

9)Expand the given binomial.

(a+2)³

1st term:

2nd term:

3rd term:

4th term:

10)Determine the coefficient that contains x¹⁰ in (x²+1)¹⁰