Additional Topics in Probability and Counting

There are 7 students in a class: 5 boys and 2 girls.
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?

• 1

How many distinguishable ways can you arrange the letters in the word finite?

• 336

• 720

• 6

• 360

You flip a nickel three times.

Find the probability that all flips will land on tails.

• ½

• ¼

• ⅙

• ⅛

A gardener has nine identical-looking tulip bulbs, of which four will produce yellow tulips and five will become pink. He randomly selects and plants four of them and then gives the rest away. When the flowers start to bloom, what is the probability that exactly two of them are yellow?

• 175/429

• 175/396

• 10/21

• 100/231

A technician is launching fireworks near the end of a show. Of the remaining fourteen fireworks, seven are blue and seven are red. If she launches eight of them in a random order, what is the probability that exactly five of them are blue ones?

• 35/143 ≈ 24.476%

• 882/2431 ≈ 36.281%

• 35/66 ≈ 37.879%

• 105/286 ≈ 36.713%

You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability that you'll have exactly three kings in your hand?

• 10/21 ≈ 47.619%

• 94/54145 ≈ 0.174%

• 490/1287 ≈ 38.073%

• 441/1144 ≈ 38.549%

A gardener has eleven identical-looking tulip bulbs, of which each will produce a different color tulip. Eight of the colors are unknown, however one will become white, one will become yellow, and one will become pink. He plants them arbitrarily in a row. When the flowers start to bloom, what is the probability that the yellow one is first in the row, the white one is second, and the pink one is at the end of the row?

• 1/990

• 1/20

• 1/72

• 1/35

A politician is about to give a campaign speech and is holding a stack of twelve cue cards, of which the first 3 are the most important. Just before the speech, she drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack?

• 1/126

• 1/2002

• 1/1320

• 1/3360

You've purchased a lottery ticket and your numbers are: 11-10-2. A lottery official randomly selects three balls from a set of thirteen balls that are numbered from #1 to #13. To win, your numbers must match the selected numbers in order. What is the probability of winning the lottery?

• 1/336

• 1/36

• 1/1716

• 1/495

A small pond contains five catfish and four bluegill. If five fish are caught at random, what is the probability that all of them are catfish?

• 1/90

• 1/126

• 1/210

• 1/56