Directions: Write the following problems in combination notation.

1. How many different sets of 6 cards each can be formed from a standard deck of 52 cards?

2. From 6 Algebra books and 8 Trigonometry books, in how many ways can Shiela selects 3 Algebra and 3 Trigonometry books to buy if all the said books are equally necessary?

3. Miguel is auditioning in one of the prestigious singing contest on television. If he is required to sing any three of the eight prepared songs, in how many ways can he make his choice?

4. A dance club needs 3 new members. If there are 5 males and 9 females applicants, in how many ways can they be selected if the new members consist of at least 2 females?

5. How many teams of at least 5 students and at most 7 students can be chosen from 15 students?

[tex]2. \: \: ( \frac{3}{6} .( \frac{3}{8} = \frac{6 \times 5 \times 4 }{3 \times 2 \times 1} \: \: \frac{ 8 \times 7 \times 6}{ 3 \times 2 \times 1 } = 1120[/tex]

[tex]3. \: \: ( \frac{3}{8} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56[/tex]

[tex]4. \: \: ( \frac{1}{5}.( \frac{2}{9} + ( \frac{0}{5}.( \frac{3}{9} = 5. \frac{9 \times 8}{2 \times 1} + 1. \frac{9 \times 8 \times 7}{3 \times 2 \times 4} = 264[/tex]

[tex]5. \: \: ( \frac{5}{15} + ( \frac{6}{15} + ( \frac{7}{15} = \frac{15 \times 14 \times 13 \times 12 \times 11}{5 \times 4 \times 3 \times 2 \times 1} + \frac{15 \times 14 \times 13 \times 12 \times 11 \times 10}{6 \times 5 \times 4 \times 3 \times 2 \times 1} + \frac{15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 5}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 4} = 14443[/tex]