SHOW YOUR COMPLETE SOLUTION FOR EACH OF THE FOLLOWING PROBLEMS. Use MS Excel Functions to help in the computation.

1. Combination In how many ways can a group of 5 members be formed from 10 girls and 8 boys

a) with no restrictions; (Ans: 8568)

b) with 3 boys and 2 girls; (Ans: 3360)

c) with all boys (Ans: 252)

2. Fundamental Principle

If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet, how many sample points are in the sample space? (Ans: 156)

3. Permutation In how many ways can 10 IT students be chosen as officers (President, Vice-President, Secretary, Treasurer, Auditor, PIO) for the IT Soc. (Ans: 151200)

4. Probability If a letter is chosen at random from the English alphabet, find the probability that the letter a) is a vowel; b) follows the letter "g".

5. Conditional Probability A random sample of 200 college students are classified below according to sex and year level:

Year Level/Sex Male Female = 38 45 11 25 30 15 20 IV 10 17

If a student is picked at random, what is the probability that

a) the student is male given that the student is a 4th year;

b) the student is a sophomore given that the student is a female.

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