Lesson test: Counting the possibilities

Counting the possibilities

1.[1p]
How many ordered sequences of two cards can be drawn from a $52$ card deck without replacement?

CorrectNot quite: 2652

2.[2p]
Why is the number of five-card poker hands $311875200 / 120$ rather than $311875200$ ?

Each set of five cards was counted once for each of its $5!$ orderings

Correct

Because $120$ cards are removed from the deck

The answer is: Each set of five cards was counted once for each of its $5!$ orderings

Because the suits are interchangeable

The answer is: Each set of five cards was counted once for each of its $5!$ orderings

Because five of the deals are impossible

The answer is: Each set of five cards was counted once for each of its $5!$ orderings

3.[2p]
How many ways are there to choose a committee of $3$ from a group of $10$ ?

CorrectNot quite: 120

4.[2p]
A lottery draws $6$ balls from $49$ with order irrelevant. How many different draws are possible?

CorrectNot quite: 13983816

5.[3p]
What is the probability that at least two of $23$ people share a birthday? Give the answer to three decimal places.

CorrectNot quite: 0.507

6.[2p]
Why does intuition underrate the birthday problem so badly?

It compares $23$ with $365$ when the relevant count is the $253$ pairs of people

Correct

It forgets leap years

The answer is: It compares $23$ with $365$ when the relevant count is the $253$ pairs of people

It assumes birthdays are uniformly spread when they are not

The answer is: It compares $23$ with $365$ when the relevant count is the $253$ pairs of people

It confuses permutations with combinations

The answer is: It compares $23$ with $365$ when the relevant count is the $253$ pairs of people

7.[3p]
Four fair dice are rolled. What is the probability that at least two show the same number? Give the answer to three decimal places.

CorrectNot quite: 0.722

8.[3p]
In how many distinguishable orders can the letters of MISSISSIPPI be arranged?

CorrectNot quite: 34650

9.[3p]
Put these five-card hands in order from most common to least common.

One pair
Three of a kind
Four of a kind
Flush
Two pair

Show the answer

a, b, c, d, e

1.[1p] How many ordered sequences of two cards can be drawn from a 52 card deck without replacement?

2.[2p] Why is the number of five-card poker hands 311875200/120 rather than 311875200?

3.[2p] How many ways are there to choose a committee of 3 from a group of 10?

4.[2p] A lottery draws 6 balls from 49 with order irrelevant. How many different draws are possible?

5.[3p] What is the probability that at least two of 23 people share a birthday? Give the answer to three decimal places.

6.[2p] Why does intuition underrate the birthday problem so badly?

7.[3p] Four fair dice are rolled. What is the probability that at least two show the same number? Give the answer to three decimal places.

8.[3p] In how many distinguishable orders can the letters of MISSISSIPPI be arranged?

9.[3p] Put these five-card hands in order from most common to least common.

1.[1p]
How many ordered sequences of two cards can be drawn from a $52$ card deck without replacement?

2.[2p]
Why is the number of five-card poker hands $311875200 / 120$ rather than $311875200$ ?

3.[2p]
How many ways are there to choose a committee of $3$ from a group of $10$ ?

4.[2p]
A lottery draws $6$ balls from $49$ with order irrelevant. How many different draws are possible?

5.[3p]
What is the probability that at least two of $23$ people share a birthday? Give the answer to three decimal places.

6.[2p]
Why does intuition underrate the birthday problem so badly?

7.[3p]
Four fair dice are rolled. What is the probability that at least two show the same number? Give the answer to three decimal places.

8.[3p]
In how many distinguishable orders can the letters of MISSISSIPPI be arranged?

9.[3p]
Put these five-card hands in order from most common to least common.