Combinations C(n,r) - One Line Questions
1.
Calculate C(7, 0). —
1
2.
What is the value of C(n, n)? —
1
3.
Calculate C(4, 4). —
1
4.
What is the value of C(8, 8)? —
1
5.
What is C(5, 5)? —
1
6.
What is the value of C(10, 10)? —
1
7.
Calculate C(8, 0). —
1
8.
Calculate C(7, 7). —
1
9.
What is C(20, 0)? —
1
10.
What is the value of C(1, 1)? —
1
11.
Evaluate C(10, 0). —
1
12.
What is C(10, 1)? —
10
13.
Evaluate C(5, 0). —
1
14.
What is the value of C(6, 1)? —
6
15.
What is C(n, 1)? —
n
16.
Calculate C(6, 5). —
6
17.
How many distinct teams of 4 players can be formed from a squad of 10 players? —
210
18.
How many ways can a president and a vice-president be chosen from a group of 10 people? —
90
19.
If C(n, 10) = C(n, 12), find n. —
22
20.
What is C(11, 4)? —
330
21.
What is C(13, 3)? —
286
22.
What is C(15, 2)? —
105
23.
Calculate C(15, 3). —
455
24.
Evaluate C(9, 2). —
36
25.
If C(n, 3) = C(n, 7), find n. —
10
26.
Evaluate C(10, 3). —
120
27.
How many ways can a group of 4 students be chosen from a class of 30 students? —
27405
28.
If C(n, 4) = C(n, 6), what is the value of n? —
10
29.
If C(n, 8) = C(n, 4), what is n? —
12
30.
What is the value of C(5, 2)? —
10
31.
In how many ways can you choose 2 fruits from a basket containing 5 different fruits? —
10
32.
Evaluate C(5, 3). —
10
33.
How many unique combinations of 3 letters can be formed from the letters A, B, C, D, E? —
10
34.
How many ways can a hand of 5 cards be dealt from a standard deck of 52 cards? —
2,598,960
35.
How many ways can a committee of 3 people be selected from a group of 8 people? —
56
36.
Evaluate C(6, 3). —
20
37.
If C(n, 2) = 28, what is the value of n? —
8
38.
How many ways can a subset of 3 elements be chosen from a set of 7 elements? —
35
39.
Calculate C(12, 5). —
792
40.
Evaluate C(10, 7). Using the property C(n, r) = C(n, n-r), this is equal to: —
C(10, 3)
41.
How many ways can a committee of 5 members be selected from 10 men and 8 women if the committee must have exactly 3 men? —
C(10, 3) * C(8, 2)
42.
How many ways can a committee of 3 men and 2 women be formed from 7 men and 5 women? —
C(7, 3) * C(5, 2)
43.
If C(n, r) = C(n, s) and r != s, then what is the relationship between n, r, and s? —
n = r + s
44.
If C(n, 5) = C(n, 5), this implies: —
No specific conclusion about n or r
45.
What is the formula for calculating the number of combinations of choosing 'r' items from a set of 'n' distinct items, denoted as C(n,r) or nCr? —
n! / (r! * (n-r)!)
46.
The number of ways to choose a subset of size k from a set of size n is given by: —
C(n, k)
47.
If a selection does not consider the order of items, it is a problem of: —
Combinations
48.
If C(n, r) = n! / (r! * (n-r)!), what is the condition for r? —
0 <= r <= n
49.
Which property of combinations states that C(n, r) = C(n, n-r)? —
Symmetry property
50.
In the combination formula C(n,r) = n! / (r! * (n-r)!), what does 'n' represent? —
The total number of distinct items available