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RD Sharma Class 11 Solutions Chapter - Combinations

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 Page 1


17. Combinations
Exercise 17.1
1 A. Question
Evaluate the following:
14
C
3
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 364.
1 B. Question
Evaluate the following:
12
C
10
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 66.
1 C. Question
Evaluate the following:
35
C
35
Answer
Page 2


17. Combinations
Exercise 17.1
1 A. Question
Evaluate the following:
14
C
3
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 364.
1 B. Question
Evaluate the following:
12
C
10
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 66.
1 C. Question
Evaluate the following:
35
C
35
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
We know that 0! = 1
? 
? 
? The value of  is 1.
1 D. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is n + 1.
1 E. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
Page 3


17. Combinations
Exercise 17.1
1 A. Question
Evaluate the following:
14
C
3
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 364.
1 B. Question
Evaluate the following:
12
C
10
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 66.
1 C. Question
Evaluate the following:
35
C
35
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
We know that 0! = 1
? 
? 
? The value of  is 1.
1 D. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is n + 1.
1 E. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
We know that 0! = 1
? 
? 
? 
? The value of  is 31.
2. Question
If 
n
C
12
 = 
n
C
5
, find the value of n.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 12?5
So, the condition(ii) must be satisfied,
? n = 12 + 5
? n = 17.
? The value of n is 17.
3. Question
If 
n
C
4
 = 
n
C
6
, find 
12
C
n
.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 4?6
So, the condition(ii) must be satisfied,
? n = 4 + 6
? n = 10.
We need to find the value of 
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Page 4


17. Combinations
Exercise 17.1
1 A. Question
Evaluate the following:
14
C
3
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 364.
1 B. Question
Evaluate the following:
12
C
10
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 66.
1 C. Question
Evaluate the following:
35
C
35
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
We know that 0! = 1
? 
? 
? The value of  is 1.
1 D. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is n + 1.
1 E. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
We know that 0! = 1
? 
? 
? 
? The value of  is 31.
2. Question
If 
n
C
12
 = 
n
C
5
, find the value of n.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 12?5
So, the condition(ii) must be satisfied,
? n = 12 + 5
? n = 17.
? The value of n is 17.
3. Question
If 
n
C
4
 = 
n
C
6
, find 
12
C
n
.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 4?6
So, the condition(ii) must be satisfied,
? n = 4 + 6
? n = 10.
We need to find the value of 
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
From (1)
? 
? 
? 
? 
? The value of  is 66.
4. Question
If 
n
C
10
 = 
n
C
12
, find 
23
C
n
.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 10?12
So, the condition(ii) must be satisfied,
? n = 10 + 12
? n = 22.
We need to find the value of 
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
From (1)
? 
? 
? 
? 
? The value of  is 23.
5. Question
If 
24
C
x
 = 
24
C
2x + 3
, find x.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
Let us use condition (i),
Page 5


17. Combinations
Exercise 17.1
1 A. Question
Evaluate the following:
14
C
3
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 364.
1 B. Question
Evaluate the following:
12
C
10
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is 66.
1 C. Question
Evaluate the following:
35
C
35
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
We know that 0! = 1
? 
? 
? The value of  is 1.
1 D. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
? 
? The value of  is n + 1.
1 E. Question
Evaluate the following:
Answer
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
Given that we need to find the value of 
From (1)
? 
? 
? 
We know that 0! = 1
? 
? 
? 
? The value of  is 31.
2. Question
If 
n
C
12
 = 
n
C
5
, find the value of n.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 12?5
So, the condition(ii) must be satisfied,
? n = 12 + 5
? n = 17.
? The value of n is 17.
3. Question
If 
n
C
4
 = 
n
C
6
, find 
12
C
n
.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 4?6
So, the condition(ii) must be satisfied,
? n = 4 + 6
? n = 10.
We need to find the value of 
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
From (1)
? 
? 
? 
? 
? The value of  is 66.
4. Question
If 
n
C
10
 = 
n
C
12
, find 
23
C
n
.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? 10?12
So, the condition(ii) must be satisfied,
? n = 10 + 12
? n = 22.
We need to find the value of 
We know that  ..... (1)
And also n! = n(n – 1)(n – 2)…………2.1
From (1)
? 
? 
? 
? 
? The value of  is 23.
5. Question
If 
24
C
x
 = 
24
C
2x + 3
, find x.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
Let us use condition (i),
? x = 2x + 3
? x = – 3
We know that for a combination 
n
C
r
,r=0 and r should be an integer which is not satisfies here,
So, the condition (ii) must be satisfied,
? 24 = x + 2x + 3
? 3x = 21
? 
? x = 7.
? The value of x is 7.
6. Question
If 
18
C
x
 = 
18
C
x + 2
, find x.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
From the problem  we can say that,
? x?x + 2
So, the condition(ii) must be satisfied,
? 18 = x + x + 2
? 2x = 16
? 
? x = 8.
? The value of x is 8.
7. Question
If 
15
C
3r
 = 
15
C
r + 3
, find r.
Answer
We know that if , then one of the following conditions need to be satisfied:
i. p = q
ii. n = p + q
Let us use condition (i),
? 3r = r + 3
? 2r = 3
? 
? 
?
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