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
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Hope it helps
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