direction of the following problems. show your solution and a separate sheet of paper

1.in how many ways can a sari-sari store owner arrange eight different can goods in a shelf if there are only five and not spaces?
2.in how many ways can 5 learners is can in circular to play a game?
3.a teacher wants to assign 4 different tasks to her for learners in how many possible ways can she do it?
4.how many distinct permutations of the letters of the word philippines are there?
5.in how many ways can she choose 4 cleaners from 20 learners?
6.lizard decided to display her six different methods on a wall in how many ways can she do this?
7.beth joanna honest and mary will arrange themselves in a row but jona and alice in cease to stand next to each other how many arrangements are possible?
8.how many distinct permutation of the letter of the word mississippi are there?
9.how many different ways can 5 students line up to purchase a new textbook reader?
10.in how many ways can she photographer arrange 7 learners in a row for picture taking to be used in their school id?

pa help naman po asap ​


Sagot :

Answer with solution:

1.

Given : n=8, r=5

Formula:

nPr = n!

(n - r)!

8P5 = 8!

(8- 5)!

= 8 x 7 x 6 x 5 x 4 x3 x2 x1

3!

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

3 x 2 x 1

= 6,720ways

2.

Given: n=5

Formula:

P = (n - 1)!

= (5 - 1)!

= 4!

= 4 x 3 x 2 x 1

= 24ways

3.

Given: n=4

Formula

P = n!

= 4!

= 4 x 3 x 2 x 1

= 24ways

4.

Given: n=11, P=3, I=3

Formula:

P = n!

P! I!

= 11!

3! 3!

= 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

(3 x 2 x 1)(3 x 2 x 1)

= 39,916,800

36

= 1,108,800 letters

5.

Given: n=20, r=4

Formula:

nPr = n!

(n - r)!

4P20 = 20!

(20 - 4)!

= 20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

16!

= 20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

= 20,922,789,888,000ways

6.

Given: n=6

Formula:

P = n!

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

= 720ways

7.

Given: n=4, r=2

Formula:

nPr = n!

(n - r)!

4P2 = 4!

(4 - 2)!

= 4 x 3 x 2 x 1

2!

= 4 x 3 x 2 x 1

2 x 1

= 12ways

8.

Given: n=11, I=4, S=4, P=2

Formula:

P = n!

I! S! P!

= 11!

4! 4! 2!

= 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

(4 x 3 x 2 x 1) (4 x 3 x 2 x 1) (2 x 1)

= 39,916,800

1,152

= 34,650 letters

9.

Given: n=5

Formula:

P = n!

= 5!

= 5 x 4 x 3 x 2 x 1

= 120 ways

10.

Given: n=7

Formula:

P = n!

= 7!

= 7 x 6 x 5 x 4 x 3 x 2 x 1

= 5,040 ways

*yung naka-bold at italic po ay crossout po..sana nagets niyo

-----------

Hope it helps

Happy to help

pa- BRAINLIEST po at pa- FOLLOW narin thanks