ECAT Mathematics
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ECAT Mathematics
Chapter 7: Permutation, Combination and Probability
86 Questions
90 Minutes
Pass: 60%+
ECAT Prep
0
n! (n factorial) equals:
A
n×(n−1)×...×2×1
B
n×(n−1)
C
n+n−1+...+1
D
n^n
1
0! =
A
0
B
1
C
undefined
D
∞
2
P(n,r) = n!/(n−r)! counts:
A
Combinations
B
Permutations of r from n
C
Subsets
D
Arrangements with repetition
3
C(n,r) = n!/(r!(n−r)!) counts:
A
Permutations
B
Ordered arrangements
C
Combinations (unordered selections)
D
Factorials
4
P(5,3) =
A
20
B
60
C
10
D
120
5
C(5,3) =
A
10
B
30
C
60
D
20
6
C(n,r) = C(n, n−r) shows:
A
Symmetry of combinations
B
Permutation formula
C
Factorial identity
D
Addition principle
7
The addition principle: if A and B are mutually exclusive, n(A or B)=
A
n(A)×n(B)
B
n(A)+n(B)
C
n(A)−n(B)
D
n(A)/n(B)
8
The multiplication principle: if task has m ways and independent task has n ways, total:
A
m+n
B
mn
C
m−n
D
m/n
9
Number of arrangements of n distinct objects:
A
n
B
n−1
C
n!
D
(n−1)!
10
Circular permutations of n distinct objects:
A
n!
B
(n−1)!
C
n!/2
D
n^n
11
P(n,n) =
A
n
B
1
C
n!
D
(n−1)!
12
Number of permutations of n objects with p identical, q identical:
A
n!
B
n!/(p!q!)
C
n!/(p+q)!
D
(n−p−q)!
13
C(n,0) =
A
0
B
n
C
1
D
n!
14
C(n,n) =
A
0
B
n
C
n!
D
1
15
Pascal's triangle identity: C(n,r) = C(n−1,r−1) + ?
A
C(n−1,r)
B
C(n,r−1)
C
C(n+1,r)
D
C(n−1,r+1)
16
Probability of event A: P(A) =
A
Favorable/Total outcomes
B
Total/Favorable
C
Favorable×Total
D
Unfavorable/Total
17
P(A) lies in:
A
(−∞,∞)
B
(0,1)
C
[0,1]
D
(−1,1)
18
P(sure event) =
A
0
B
0.5
C
1
D
∞
19
P(impossible event) =
A
0
B
0.5
C
1
D
−1
20
P(A') = 1 − P(A) is:
A
Addition law
B
Complement law
C
Multiplication law
D
Bayes theorem
21
For mutually exclusive A and B: P(A∪B)=
A
P(A)×P(B)
B
P(A)+P(B)
C
P(A)−P(B)
D
P(A)/P(B)
22
General addition law: P(A∪B)=
A
P(A)+P(B)
B
P(A)+P(B)−P(A∩B)
C
P(A)×P(B)
D
P(A|B)×P(B)
23
For independent events A and B: P(A∩B)=
A
P(A)+P(B)
B
P(A)−P(B)
C
P(A)×P(B)
D
P(A|B)
24
P(A|B) = P(A∩B)/P(B) is:
A
Joint probability
B
Conditional probability
C
Complementary probability
D
Marginal probability
25
A fair coin is tossed. P(Head) =
A
0
B
1
C
1/2
D
1/4
26
A fair die is rolled. P(even number) =
A
1/6
B
1/2
C
1/3
D
2/3
27
Two dice rolled. P(sum=7) =
A
1/6
B
5/36
C
6/36=1/6
D
7/36
28
From a deck of 52 cards, P(Ace) =
A
1/13
B
4/52=1/13
C
1/4
D
4/13
29
C(10,4) =
A
210
B
120
C
252
D
180
30
Number of ways to arrange letters of MATH:
A
24
B
12
C
4
D
16
31
Number of ways to arrange letters of MISS (2 S):
A
12
B
24
C
4
D
6
32
P(A) + P(A') =
A
0
B
2
C
1
D
P(A)
33
A bag has 3 red and 4 blue balls. P(drawing red) =
A
3/7
B
4/7
C
3/4
D
1/2
34
P(A|B) when A and B independent =
A
P(B)
B
P(A)+P(B)
C
P(A)
D
P(A)P(B)
35
Bayes theorem: P(A|B) =
A
P(B|A)P(A)/P(B)
B
P(A)P(B)
C
P(A∪B)
D
P(B)/P(A)
36
Sample space S for tossing 2 coins:
A
{{H,T}}
B
{{HH,HT,TH,TT}}
C
{{H,T,HH}}
D
{{H,H,T,T}}
37
P(at least one head in 2 tosses) =
A
1/4
B
1/2
C
3/4
D
1
38
Number of subsets of {a,b,c,d} of size 2:
A
6
B
4
C
12
D
8
39
How many 3-digit numbers from {1,2,3,4,5} without repetition?
A
60
B
120
C
20
D
100
40
How many ways to select committee of 3 from 7 people?
A
35
B
21
C
42
D
210
41
P(A∩B)=0 means A and B are:
A
Independent
B
Mutually exclusive
C
Complementary
D
Exhaustive
42
Experiment: selecting card from deck. Sample space size:
A
4
B
13
C
52
D
26
43
A number is selected from 1-10. P(prime) =
A
2/5
B
3/5
C
4/10
D
1/2
44
Sum of all probabilities in sample space =
A
0
B
P(A)
C
1
D
∞
45
Number of ways to choose 4 items from 4:
A
1
B
4
C
24
D
0
46
C(n,1) =
A
1
B
n
C
n!
D
n−1
47
Permutation of 0 from n:
A
0
B
1
C
n
D
n!
48
In how many ways can 5 people sit in a row?
A
5
B
20
C
25
D
120
49
How many ways to arrange 3 from 5 people in a line?
A
15
B
20
C
60
D
120
50
Experiment of rolling die: P(number > 4) =
A
1/3
B
1/2
C
2/3
D
1/6
51
Number of ways to arrange letters of LEVEL (3 non-distinct):
A
60
B
30
C
20
D
120
52
P(both events occur) when P(A)=0.4, P(B)=0.3, independent:
A
0.7
B
0.1
C
0.12
D
0.5
53
P(A or B) when P(A)=0.5, P(B)=0.4, P(A∩B)=0.2:
A
0.9
B
0.2
C
0.7
D
1.1
54
How many 4-letter words from {a,b,c,d,e} with repetition?
A
20
B
120
C
625
D
256
55
Number of diagonals of a hexagon (6-sided):
A
9
B
12
C
6
D
15
56
P(drawing face card) from deck:
A
1/13
B
3/13
C
4/52
D
12/52=3/13
57
P(A) = 3/5. P(A') =
A
2/5
B
3/5
C
1/5
D
4/5
58
P(A or B) when A and B mutually exclusive, P(A)=1/3, P(B)=1/4:
A
7/12
B
1/12
C
1/4
D
1/3
59
An event that cannot fail is called:
A
Impossible event
B
Sure event
C
Complementary event
D
Random event
60
P(drawing red from bag: 3 red, 2 blue, 5 green):
A
3/10
B
1/2
C
2/5
D
5/10
61
In how many ways can 6 books be arranged on shelf?
A
36
B
720
C
120
D
216
62
How many 2-digit numbers using {1,2,3} without repetition?
A
6
B
9
C
3
D
12
63
Odds in favor of event A: P(A)=3/4:
A
3:1
B
1:3
C
3:4
D
4:3
64
C(8,3) =
A
56
B
28
C
168
D
40
65
C(8,5) =
A
56
B
28
C
168
D
40
66
Number of ways to divide 6 people into 2 equal groups:
A
10
B
15
C
30
D
20
67
How many ways to form a team of 2 boys and 3 girls from 4 boys and 5 girls?
A
60
B
120
C
240
D
480
68
P(drawing 2 kings from deck without replacement):
A
1/221
B
4/51
C
1/13
D
2/52
69
Mutually exclusive events: A∩B=
A
S
B
A
C
∅
D
B
70
P(neither A nor B) when P(A)=0.3, P(B)=0.4, independent:
A
0.42
B
0.12
C
0.58
D
0.7
71
FACT: Σ C(n,k) for k=0 to n =
A
n
B
n!
C
2^n
D
n^2
72
How many ways to choose president, VP, secretary from 10 people?
A
120
B
720
C
30
D
10×9×8=720
73
P(rolling sum ≥ 11 with two dice) =
A
1/12
B
3/36
C
1/9
D
2/36
74
Arrangement of n things in circle if clockwise = anticlockwise:
A
n!/2
B
(n−1)!/2
C
(n−1)!
D
n!
75
P(A|B) × P(B) =
A
P(A)
B
P(B)
C
P(A∩B)
D
P(A∪B)
76
C(15,7) = C(15, ?)
A
7
B
8
C
15
D
6
77
Number of handshakes among 10 people:
A
45
B
90
C
10
D
100
78
P(drawing heart or king) from deck:
A
17/52
B
4/13
C
16/52
D
13/52
79
Geometric probability: P = favorable length/total length applies to:
A
Discrete events
B
Continuous uniform experiments
C
Card experiments
D
Coin experiments
80
P(at least 2 heads in 3 tosses) =
A
1/2
B
3/8
C
4/8
D
7/8
81
From 5 men 3 women, choose committee of 3 with at least 1 woman:
A
45
B
25
C
46
D
30
82
How many even 3-digit numbers from {1,2,3,4,5} without repetition?
A
24
B
20
C
12
D
48
83
P(same number on 2 dice) =
A
1/6
B
1/36
C
2/6
D
1/12
84
Total number of outcomes when 3 coins tossed:
A
6
B
8
C
4
D
3
85
P(all heads in 3 tosses) =
A
1/8
B
3/8
C
1/2
D
1/4
0
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