Combinatorics

2010007003

Level:

The shop offers a selection of

8

types of ice-lollies? (All types in numbers over

4

pieces.). In how many ways can we choose

4

ice-lollies?

\frac{11!}{4! 7!} = 330

\frac{8!}{4! 4!} = 70

\frac{8!}{4!} = 1680

4^{8} = 65536

2010007602

Level:

What is the coefficient at

x^{5}

in the expansion of

(1 - 2 x)^{11}

- 14 784

14 784

7 374

- 7 374

2010007603

Level:

Find the constant term in the expansion of

{(2 x^{2} - 3)}^{25}

- 3^{25}

3^{25}

2^{25}

- 2^{25}

9000139704

Level:

There are

5

different kinds of cakes in a shop. Find the number of possibilities how to buy

8

cakes in this shop. (There is more than

8

cakes of each kind available.)

\frac{12!}{8! 4!} = 495

5! 8! = 4 838 400

5^{8} = 390 625

\frac{8!}{5! 3!} = 56

9000139710

Level:

The wallet contains nine coins: three

1

-Euro coins, three

2

-Euro coins and three

5

-Euro coins. How many different amounts can be paid if we have to pay the amount exactly and use just three coins for this payment?

\frac{5!}{3! 2!} = 10

\frac{5!}{3!} = 20

3^{3} = 27

3! = 6

9000153901

Level:

Find the number of ways how to distribute

8

identical balls among

5

persons so that each of them gets at least one ball.

(\binom{7}{3}) = 35

5^{3} = 125

(\binom{12}{5}) = 792

(\binom{12}{8}) = 495

9000153902

Level:

Find the number of ways how to distribute

8

identical balls among

5

persons.

(\binom{12}{8}) = 495

5^{8} = 390625

(\binom{8}{5}) = 56

(\binom{12}{5}) = 792

9000153903

Level:

Find the number of ways how to distribute

8

mutually different balls among

5

persons.

5^{8} = 390625

\frac{8!}{3!} = 6720

8^{5} = 32768

(\binom{12}{8}) = 495

9000153905

Level:

Find the number of ways how to distribute

5

identical balls among

8

persons.

(\binom{12}{5}) = 792

8^{5} = 32768

(\binom{12}{8}) = 495

\frac{8!}{3!} = 6720

9000153906

Level:

Find the number of ways how to distribute

5

identical balls among

8

persons so that no persons gets more than one ball.

\frac{8!}{5! 3!} = 56

\frac{8!}{3!} = 6 720

(\binom{12}{8}) = 495

(\binom{12}{5}) = 792

2010007003

2010007602

2010007603

9000139704

9000139710

9000153901

9000153902

9000153903

9000153905

9000153906

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