Answer Happy

1. (10 points) In a certain state, license plates consist of 4
English letters. Repetition of symbols is not allowed. How many
license plates contain at least 3 vowels? Justify! (There exist 26
letters in the English alphabet, of which 5 are vowels.)
2. (10 points) A store has balloons of 10 colors; one of the
colors is blue. Balloons of the same color are indistinguishable.
The store has at least 50 balloons of each color. How many
different ways can you choose 50 balloons, such that at least 30 of
them are blue?
Justify all answers and show your work unless stated otherwise. In questions requiring justification, answers without sufficient justification will be granted no credit Student's Name: 1. (10 points) In a certain state, license plates consist of 4 English letters. Repetition of symbols is not allowed. How many license plates contain at least 3 vowels? Justify! (There exist 26 letters in the English alphabet, of which 5 are vowels.) A. 21. ) . (4!) - () - (4!) = 4920) B. 21. 3). (4!) + () . (4!)(=5160) C. (15) . (4!) – (5) . ) (3!) = 3946800) D. (5) . () (4!) + (3) . ) . (3!)=11840400) E. None of the above 2. (10 points) A store has balloons of 10 colors; one of the colors is blue. Balloons of the same color are indistinguishable. The store has at least 50 balloons of each color. How many different ways can you choose 50 balloons, such that at least 30 of them are blue? A. (20+20-1)(=10015005) B. (30+30-1)(=211915132) C. (50430-1) – (30+30-1)(= 12353756129) D. (50+50-?) - (20+20-1)(= 12555656256) E. None of the above 10-