In how many ways you can arrange 10 movie discs on a shelf?

10 × 8 ! × 9 10\times8!\times9 1 0 × 8 ! × 9

10 × 9 ! × 8 10\times9!\times8 1 0 × 9 ! × 8

10 ! × 9 × 8 10!\times9\times8 1 0 ! × 9 × 8

10 × 9 × 8 10\times9\times8 1 0 × 9 × 8

How many different arrangements can be formed from UNIVERSITY?

10 ! × 2 10!\times2 1 0 ! × 2

How many different arrangements can be made from MISSISSIPPI?

11 ! 2 ! × 4 ! × 4 ! \frac{11!}{2!\times4!\times4!} 2 ! × 4 ! × 4 ! 1 1 !

11 ! ( 2 + 4 + 4 ) ! \frac{11!}{\left(2+4+4\right)!} ( 2 + 4 + 4 ) ! 1 1 !

11 ! 2 ! + 4 ! + 4 ! \frac{11!}{2!+4!+4!} 2 ! + 4 ! + 4 ! 1 1 !

4 ! × 4 ! × 2 ! × 1 ! 4!\times4!\times2!\times1! 4 ! × 4 ! × 2 ! × 1 !

How many different arrangements can be made from the word INTERNATIONALIZATION?

20 ! 4 ! × 4 ! × 3 ! × 3 ! × 2 ! \frac{20!}{4!\times4!\times3!\times3!\times2!} 4 ! × 4 ! × 3 ! × 3 ! × 2 ! 2 0 !

20 ! 4 ! × 4 ! × 3 ! × 2 ! × 2 ! \frac{20!}{4!\times4!\times3!\times2!\times2!} 4 ! × 4 ! × 3 ! × 2 ! × 2 ! 2 0 !

20 ! 4 ! × 4 ! × 3 ! × 3 ! \frac{20!}{4!\times4!\times3!\times3!} 4 ! × 4 ! × 3 ! × 3 ! 2 0 !

20 ! 4 ! × 3 ! × 3 ! × 3 ! \frac{20!}{4!\times3!\times3!\times3!} 4 ! × 3 ! × 3 ! × 3 ! 2 0 !

How many ways of picking only one item from 5 books and 4 pens?

5 ! × 4 ! 5!\times4! 5 ! × 4 !

How many ways of picking one book and one pen from 5 books and 4 pens?

5 ! × 4 ! 5!\times4! 5 ! × 4 !

What is the formula of Permutation?

P r n = n ! ( n − r ) ! P_r^n=\frac{n!}{\left(n-r\right)!} P r n = ( n − r ) ! n !

P r n = n ! ( n + r ) ! P_r^n=\frac{n!}{\left(n+r\right)!} P r n = ( n + r ) ! n !

P r n = n ! r ! P_r^n=\frac{n!}{r!} P r n = r ! n !

P r n = n ! r ! ( n − r ) ! P_r^n=\frac{n!}{r!\left(n-r\right)!} P r n = r ! ( n − r ) ! n !

What is the formula of Combination?

C r n = n ! r ! ( n − r ) ! C\ _r^n=\frac{n!}{r!\left(n-r\right)!} C r n = r ! ( n − r ) ! n !

C r n = n ! ( n − r ) ! C\ _r^n=\frac{n!}{\left(n-r\right)!} C r n = ( n − r ) ! n !

C r n = n ! ( n + r ) ! C\ _r^n=\frac{n!}{\left(n+r\right)!} C r n = ( n + r ) ! n !

C r n = n ! r ! C\ _r^n=\frac{n!}{r!} C r n = r ! n !

Select 3 out of 5 who get buscuits

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

Select 3 out of 5 who get biscuits. One of them gets with cheese, another one gets with chocolate and the last one - salty biscuits

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

Arrange 7 different pens between 7 people out of 9.

9 ! 7 ! 2 ! \frac{9!}{7!2!} 7 ! 2 ! 9 !

Select 4 people out of 7 to give them pens.

7 ! 4 ! 3 ! \frac{7!}{4!3!} 4 ! 3 ! 7 !

Teacher selects 2 students out of 19 for duty. One of them has to take out the trash and another - wipes the board. How many possible ways?

19 ! 17 ! \frac{19!}{17!} 1 7 ! 1 9 !

19 ! 2 ! \frac{19!}{2!} 2 ! 1 9 !

19 ! 17 ! 2 ! \frac{19!}{17!2!} 1 7 ! 2 ! 1 9 !

18 ! 16 ! \frac{18!}{16!} 1 6 ! 1 8 !

You and your 13 friends ate pizza. 3 pieces left. How many ways of the distribution of these pieces between you, provided that one piece should be eaten only by 1 person?

14 ! 11 ! 3 ! \frac{14!}{11!3!} 1 1 ! 3 ! 1 4 !

13 ! 10 ! 3 ! \frac{13!}{10!3!} 1 0 ! 3 ! 1 3 !

13 ! 10 ! \frac{13!}{10!} 1 0 ! 1 3 !

14 ! 11 ! \frac{14!}{11!} 1 1 ! 1 4 !

Permutation and Combination

Authored by Nurken Otegen

Mathematics

10th - 11th Grade

CCSS covered

Used 12+ times

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40 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which is a factorial?

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Work out 4!

256

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Work out 6!

46656

720

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Calculate: $\frac{7!}{5!}$

720

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Calculate $\frac{10!}{7!}$

900

720

$\frac{10}{7}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Evaluate: (11 - 10)!

720

600

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Evaluate: 4! - 2!

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\frac{5!}{3!6!}\times\frac{6!}{2!5!}$

$\frac{1}{5!}$

$\frac{1}{6}$

$\frac{1}{6!}$

$\frac{1}{12}$

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