# Class 11 RD Sharma Solutions- Chapter 17 Combinations- Exercise 17.1 | Set 1

• Last Updated : 11 Feb, 2021

### i) 14C3

Solution:

We know that    nCr=n!/(n-r)!r!

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=>14C3=14!/(14-3)!3!

=14!/11!3!

=14x13x12/3x2x1

=364

### ii) 12C10

Solution:

= 12!/(12-10)!10!

= 12!/2!10!

= 12×11/2×1

= 66

### iii) 35C35

Solution:

= 35!/(35-35)!35!

= 1

### iv) n+1Cn

Solution:

= (n+1)!/(n+1-n)!n!

= (n+1)!/n!

= n+1

### v) 5

Solution:

5Cr=5C1+5C2+5C3+5C4+5C5

r = 1

= 5+10+10+5+1

= 31

### Question 2. If nC12=nC5, find the value of n.

Solution:

Given that nC12=nC5.

We know that two combinations will be equal when the sum of their r’s is equal to n.

=>n=12+5=17.

### Question 3. If nC4=nC6 , find 12Cn.

Solution:

=>n=6+4=10

=>12C10=12!/10!2!

=12×11/2

=66

### Question 4. If nC10=nC12 , 23Cn.

Solution:

n = 10+12=22

=>23C22 = 23!/22!1!

= 23

Solution:

24 = x+2x+3

24 = 3x+3

21 = 3x

x = 21/3

x = 7

Solution:

18 = x+x+2

18 = 2x+2

16 = 2x

x = 8

Solution:

15 = 3r+r+3

15 = 4r+3

12 = 4r

r = 3

### Question 8. If 8Cr–7C3=7C2, find r.

Solution:

Given 8Cr7C3=7C2

=>8Cr=7C2+7C3

We know that nCr+nCr-1=n+1Cr

=>8Cr=8C3

=>r=3

### Question 9. If 15Cr:15Cr-1 = 11:5, find r.

Solution:

15Cr/15Cr-1=11/5

(15!/(15-r)!r!)/(15!/(15-r+1)!(r-1)!)=11/5

15-r+1/r = 11/5

5(16-r) = 11r

80-5r = 11r

16r = 80

r = 5

### Question 10. If n+2C8:n-2P4=57:16, find n.

Solution:

We know that nPr=n!/(n-r)!

=>((n+2)!/(n+2-8)!8!)/((n-2)!/(n-2-4)!)=57/16

=>(n+2)(n+1)(n)(n-1)/8!=57/16

=>(n-1)n(n+1)(n+2)=(57/16)8!

=>(n-1)n(n+1)(n+2)=57×7!/2

=>(n-1)n(n+1)(n+2)=57x7x6x5x4x3

=>(n-1)n(n+1)(n+2)=19x3x7x6x5x4x3

=>(n-1)n(n+1)(n+2)=19x18x20x21

=>n=19

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