Editorial - Matwa - Latihan PAS
original link: https://corca.app/doc/rMEk8UDA9pFCULdl_78on
Latihan PAS 1
Problem 1
1/6!*(5/7-1+24/56)=1/5040
Problem 2
n=2
Problem 3
8!/(4!4!)
Problem 4
40320/30=1344
Problem 5
8!/(4!2!2!)=420
Problem 6
8!/(2!6!)=28
Problem 7
n!/((n-4)!4!)=n!/((n-3)!3!)
24(n-4)!=6(n-3)!
6*n=42
n=7
Problem 8
28⋅4+56=168
Problem 9
p=6
Problem 10
(4⋅3)*(4⋅3)=144
Problem 11
81*a4+108*a3*b+54*a2*b2+2*a*b3+b4
Problem 12
7!/(3!4!)=35
Problem 13
((n-2)*(n-3)(n-4)!)/(n-4)!=20
(n-2)*(n-3)=20
n=7
Problem 14
8!/(2!6!)⋅5=140
Problem 15
6!=720
Latihan PAS 2
Problem 1
n=3⋅5⋅4⋅3=180
Problem 2
n=6⋅2⋅5⋅4⋅3⋅2⋅1=1440
Problem 3
n=9!/(2!⋅2!)=90720
Problem 4
n=7!-6!⋅2=3600
Problem 5
10!/(6!4!)⋅8!/(2!6!)+10!/(5!5!)⋅8+10!/(6!4!)=8106
Problem 6
5!/(3!2!)⋅7!/(4!3!)⋅7!=1764000
Problem 7
3⋅4⋅3⋅4⋅2=288
Problem 8
9!/(3!3!3!)=1680
Problem 9
5!/(2!3!)⋅4+5!/(3!2!)=50
P=50/9!/(3!6!)=25/42
Latihan PAS 3
Problem 1
P=(([5],[2])⋅([3],[3])+([5],[4])⋅([3],[1]))/([8],[5])=25/56
Problem 2
(n+1)!/(n-2)!=n!/(n-4)!
(n+1)*(n)*(n-1)=n*(n-1)*(n-2)*(n-3)
n+1=(n-2)*(n-3)
n={1,+5}
∴n=5
Problem 3
(n-1)*(n-2)=110
n={-9,+12}
∴n=12
Problem 4
n=2!3!4!⋅2=576
Problem 5
10⋅10⋅10⋅10=10000
Problem 6
6⋅5⋅4⋅3=360
Problem 7
S=52!/(2!(52-2)!)=1326
A=4!/(2!*(4-2!))=6
P=6/1326=1/221
Problem 8
2+3
3+2
1+4
4+1
P=4/36=1/9
(P_c)=1-1/9=8/9
Problem 9
P=9/15=3/5
Problem 10
P=(9⋅8⋅7)/(3⋅2⋅1)/(15⋅14⋅13)/(3⋅2⋅1)=12/65