Combinatorics

Combinatorics

Multiple Choice

Six friends (A, B, C, D, E, F, G) go to the theatre and they are allocated adjacent seats. How many different ways can they sit down?

• 5!

• 6!*2

• $$\frac{6!}{6}$$

• 6!

Multiple Choice

How many ways can they sit if C and D want to sit next to each other?

• 2*6!

• 2*5!

• 5*5

• 2*4!

Multiple Choice

How many ways can they sit down if A, B and C want to sit next to each other in any order?

• 3*4!

• 3!*5!

• 3!*4!

• 3*5!

Multiple Choice

Numbers 0,1,2,3,4,5,6,7,8,9 are given. In how many arrangements can 4,5,6 be next to each other in an increasing order?

• 10!

• 3*9!

• 3*8!

• 8!

Multiple Choice

There are 12 watches from different brands. Nasim would like to have 7 watches from different brands. In how many different ways can he pick?

• 12*11*10*9*8*7

• $$\frac{12!}{5!}$$

• $$\frac{12!}{7!}$$

• $$12^7$$

Multiple Choice

How many 8-digit numbers can be formed using all of the following 8 digits:

0, 1, 2, 3, 4, 5, 6, 7?

• 7*7!

• 8!

• 8*7!

• 7*8!

Multiple Choice

How many 6-digit numbers can be formed using the following digits: 

1 1 1 2 2 3?

• $$\frac{6!}{3\times2}$$

• $$\frac{6!}{3!\times2!}$$

• $$6!\div3!\times2!$$

• $$6!\div3\times2$$

Multiple Choice

Digits 4,8,9,2 are given. How many different 3-digit numbers can we construct if each digit can be used more than once?

• 4!

• $$4^4$$

• $$4^3$$

• 3!

Multiple Choice

10 boys and 9 girls go to Ted Talk together. They all sit next to each other.

In how many ways can they sit?

• 10!*9!

• 10!*2

• 10!*9!*2

• 19!

Multiple Choice

How many 4-digit passwords can we create using the digits of the decimal system if we can use each digit at most once?

• $$\frac{10!}{4!}$$

• $$\frac{10!}{6!}$$

• $$4^{10}$$

• $$10^4$$

Multiple Choice

How many 4-digit passwords can we create using the digits of the decimal system if we can use each digit more than once?

• $$\frac{10!}{4!}$$

• $$\frac{10!}{6!}$$

• $$4^{10}$$

• $$10^4$$

Multiple Choice

During PE lesson, Ms. Judit wants to create 2 volleyball teams. There are 15 girls in the class, so we need a team with 7 and another team with 8 members. In how many ways can Ms. Judit form the 2 teams?

• $$\frac{15!}{7!\times8!}$$

• $$\frac{15!}{7!}$$

• 15*14*13*12*11*10*9

• $$\frac{15!}{8!}$$

Multiple Choice

During the oral examination, Mr. Sandor would like to ask from 3 students, and the remaining 7 are taking a written quiz. How many different arrangements are there if the order at the oral part does matter?

• 10*9*8

• $$\frac{10!}{3!\times7!}$$

• $$\frac{10!}{3!}$$

• 3!*7*

Multiple Choice

You want to sit at a circular table with 6 of your friends and your brother. How many ways can you sit if you want to sit next to your brother?

• $$\frac{8!}{8}$$

• $$2\times\frac{8!}{8}$$

• $$2\times\frac{7!}{7}$$

• $$\frac{7!}{7}$$

Multiple Choice

Mr. Bálint needs 3 boys from 11.B. In how many different ways can he choose them if there are 8 girls in the class and there are 18 students in total?

• $$\frac{18!}{10!\times8!}$$

• $$\frac{10!}{3!\times7!}$$

• $$\frac{18!}{10!}$$

• $$\frac{18!}{8!}$$