Combinatorics

B

1

What is the probability of rolling a 6 with 1 fair die?

1/6

25

How many ways are there to arrange 2 identical blue balls and 1 red ball in a line?

3

100

If Al and Bl are equally skilled at connect 4, meaning that they have the same probability of winning, and the probability that they draw is 1/2, what is the probability that Al would win more games than Bl in a series of 2?

5/16

125

Alec draws 4 cards from a standard 52-card deck (without the Joker). What is the probability that the 4 cards all have different numbers on them? You may choose to present the final result as a fraction with relatively prime numerators and denominators that are not necessarily calculated to the exact value (for example 28*25/729 is a valid solution)

17*5*49/16*44*4

(which equates to 4165/6336)

I

1

How many ways can we construct a meal of 1 soup and 1 main course from 3 soups and 4 main courses?

12

25

What is the probability of obtaining 2 heads from 3 coin throws?

3/8

100

In how many ways can we distribute 16 balls into 3 urns if the first urn must receive at least 1 ball, the second at least 2, and the third at least 3?

66

125

In how many ways can we distribute 10 balls into 3 urns if the first urn may receive a MAXIMUM of 3 balls, the second urn may receive a MAXIMUM of 4 balls, and the third urn may receive a MAXIMUM of 5 balls?

6

N

1

How many ways are there to arrange 4 balls of different colors in a line?

24

25

How many ways are there to arrange 2 identical blue balls and 1 red ball in a circle?

1

100

How many ways can we arrange 3 blue balls and 4 orange balls in a straight line?

35

125

What is the probability of drawing cards with adjacent values (for example 9 and 10) when drawing 2 cards from a standard 52-card suite (without the joker)?

32/221

G

1

How many ways are there to arrange 4 balls of different colors in a circle?

6

25

How many ways are there to arrange a red ball, and blue ball, and a green ball in a circle, provided that the red ball must be adjacent to the green ball?

6

(it's all the same it's all the same)

100

Al and Bl draw cards from a suite. Al wins if the card is prime, and Bl wins if the card is composite. Find the value of (the probability of Al winning)/(the probability of Bl winning). Kings count as 13, Queens as 12, and Jacks as 11.

1

125

A set of dice results are said to be "harmonious" if no repeat values occur. Al repeatedly rolls a fair die. Determine the probability that the dice results will still be harmonious after 3 rolls.

5/9