- A bag contains 6 green and 9 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 4?
Answer
#Green drawn is 3, 2 1 0
choose(6,3)*choose(9,2)+ choose(6,2)*choose(9,3)+ choose(6,1)*choose(9,4)+ choose(6,0)*choose(9,5)
## [1] 2862
Answer
- A certain congressional committee consists of 14 senators and 13 representatives. How many ways can a subcommittee of 7 be formed if at least 4 of the members must be senators?
#No of senator 4 5 6 7
choose(14,4)*choose(13,3)+ choose(14,5)*choose(13,2)+ choose(14,6)*choose(13,1)+choose(14,7)*choose(13,0)
## [1] 484913
- If a coin is tossed 2 times, and then a standard six-sided die is rolled 4 times, and finally a group of three cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer
#Possibilities each time 2 6 porb of 3 from 52
(2^2)*(6^4)*choose(52,3)
## [1] 114566400
- 3 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a heart? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer
# non hearts total
1-(choose(39,3)/choose(52,3))
## [1] 0.5864706
- Leanne is picking out some movies to rent, and she is primarily interested in children’s movies and comedies. She has narrowed down her selections to 18 children’s movies and 7 comedies.
Step 1. How many different combinations of 3 movies can she rent?
Answer
choose(25,3)
## [1] 2300
Step 2. How many different combinations of 3 movies can she rent if she wants at least one comedy?
Answer
choose(7,1)*choose(18,2)+ choose(7,2)*choose(18,1)+ choose(7,3)*choose(18,0)
## [1] 1484
- Mallory is planting trees along her driveway, and she has 3 beech trees and 3 eucalyptus trees to plant in one row. What is the probability that she randomly plants the trees so that all 3 beech trees are next to each other and all 3 eucalyptus trees are next to each other? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer
2/(factorial(6)/(factorial(3)*factorial(3)))
## [1] 0.1