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Quiz

Lesson 1: Counting Principle, Permutations (nPr) and Combinations (nCr) — Picture questions (exam style)

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  • Questions count: 32
  • Passing grade: 60%
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1.
In how many ways can 8 people sit in a row (figure) if two particular people sit at the two ends?
In how many ways can 8 people sit in a row (figure) if two particular people sit at the two ends?
2880
720
40320
1440
2.
In (1 + x)n the ratio of the coefficients of T_4 and T_3 is 3. Which option is correct?
In (1 + x)ⁿ the ratio of the coefficients of T_4 and T_3 is 3. Which option is correct?
n = 11, number of terms = 13
n = 11, number of terms = 11
n = 5, number of terms = 12
n = 11, number of terms = 12
3.
A committee of 3 must include at least one girl from the group shown. How many ways?
A committee of 3 must include at least one girl from the group shown. How many ways?
354
702
280
364
4.
In the expansion shown, what is the coefficient of x2?
In the expansion shown, what is the coefficient of x^2?
6
-54
54
-108
5.
How many 3-digit numbers greater than 400, with different digits, can be made from the cards?
How many 3-digit numbers greater than 400, with different digits, can be made from the cards?
60
30
24
10
6.
In how many ways can 7 people sit in a row (figure) if two particular people sit at the two ends?
In how many ways can 7 people sit in a row (figure) if two particular people sit at the two ends?
5040
120
240
480
7.
A committee of 3 must contain exactly 2 girl(s) from the group shown. How many ways?
A committee of 3 must contain exactly 2 girl(s) from the group shown. How many ways?
84
18
36
9
8.
How many 4-digit numbers greater than 5000, with different digits, can be made from the cards?
How many 4-digit numbers greater than 5000, with different digits, can be made from the cards?
12
24
1
6
9.
In how many ways can 5 people sit in a row (figure) if two particular people sit at the two ends?
In how many ways can 5 people sit in a row (figure) if two particular people sit at the two ends?
6
24
12
120
10.
A committee of 6 is chosen from the group shown. How many ways?
A committee of 6 is chosen from the group shown. How many ways?
5880
8568
18564
13366080
11.
A committee of 4 must contain exactly 3 girl(s) from the group shown. How many ways?
A committee of 4 must contain exactly 3 girl(s) from the group shown. How many ways?
5040
3876
840
94
12.
How many 3-digit numbers with different digits can be made from the cards shown?
How many 3-digit numbers with different digits can be made from the cards shown?
24
49
28
33
13.
In the expansion shown, what is the coefficient of x2?
In the expansion shown, what is the coefficient of x^2?
22
21
18
42
14.
How many 4-digit numbers greater than 3000, with different digits, can be made from the cards?
How many 4-digit numbers greater than 3000, with different digits, can be made from the cards?
240
150
15
360
15.
In how many ways can 6 people sit in a row (figure) if two particular people sit at the two ends?
In how many ways can 6 people sit in a row (figure) if two particular people sit at the two ends?
24
720
48
96
16.
A committee of 6 is chosen from the group shown. How many ways?
A committee of 6 is chosen from the group shown. How many ways?
1723
1716
1287
1235520
17.
What is the term independent of x in the expansion shown?
What is the term independent of x in the expansion shown?
-4320
4860
-4860
15
18.
How many 3-digit numbers greater than 300, with different digits, can be made from the cards?
How many 3-digit numbers greater than 300, with different digits, can be made from the cards?
20
60
120
80
19.
A committee of 6 is chosen from the group shown. How many ways?
A committee of 6 is chosen from the group shown. How many ways?
20160
35
56
28
20.
What is the term independent of x in the expansion shown?
What is the term independent of x in the expansion shown?
-61236
84
30618
61236
21.
A committee of 5 must include at least one girl from the group shown. How many ways?
A committee of 5 must include at least one girl from the group shown. How many ways?
1584
792
807
794
22.
A committee of 3 is chosen from the group shown. How many ways?
A committee of 3 is chosen from the group shown. How many ways?
700
286
1716
78
23.
In the expansion shown, what is the coefficient of x1?
In the expansion shown, what is the coefficient of x^1?
16
64
-64
4
24.
In the expansion shown, what is the coefficient of x2?
In the expansion shown, what is the coefficient of x^2?
-20412
28
17496
20412
25.
What is the term independent of x in the expansion shown?
What is the term independent of x in the expansion shown?
-146
126
-84
84
26.
How many even 4-digit numbers with different digits can be made from the cards?
How many even 4-digit numbers with different digits can be made from the cards?
360
15
180
240
27.
A committee of 5 must include at least one girl from the group shown. How many ways?
A committee of 5 must include at least one girl from the group shown. How many ways?
1996
1983
1981
3962
28.
A committee of 5 must include at least one girl from the group shown. How many ways?
A committee of 5 must include at least one girl from the group shown. How many ways?
1260
461
456
462
29.
A committee of 3 is chosen from the group shown. How many ways?
A committee of 3 is chosen from the group shown. How many ways?
78
1716
120
286
30.
In the expansion shown, what is the coefficient of x8?
In the expansion shown, what is the coefficient of x^8?
9
27
-27
324
31.
In the expansion shown, what is the coefficient of x3?
In the expansion shown, what is the coefficient of x^3?
53
112
56
57
32.
How many 4-digit numbers greater than 3000, with different digits, can be made from the cards?
How many 4-digit numbers greater than 3000, with different digits, can be made from the cards?
28
24
33
49
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