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Chapter 17: Combinations – Exercise 17.1 Combinations – Exercise – 17.1 – Q.1(i) Combinations – Exercise – 17.1 – Q.1(ii) Combinations – Exercise – 17.1 – Q.1(iii) Combinations – Exercise – 17.1 – Q.1(iv) Combinations – Exercise – 17.1 – Q.1(v) = 5 + 10 +10 + 5 + 1 = 31 Combinations – Exercise – 17.1 – Q.2 Hence n = n r = 12 and 5 Applying formula nCp = nCq = n Then p + q = n ⟹ nC12 = nC5 12 + 5 = n ⟹ n = 17 Combinations – Exercise – 17.1 – Q.3 If nCp = nCq Then p + q = n ⟹ nC4 = nC6 4 + 6 = n ⟹ n = 10 then 12Cn = 12C10 Applying (i) Combinations – Exercise – 17.1 – Q.4 If nCp = nCp The p + q = n ⟹ nC10 = nC12 10 + 12 = n ⟹ n = 22 Find 23Cn ⟹ 23C22 = 23 Combinations – Exercise – 17.1 – Q.5 If nCp = nCr then P + r = n ∴ x + 2x + 3 = 24 3x = 21 x = 7 Combinations – Exercise – 17.1 – Q.6 If nCp = nCq ⟹ p + q = n also Cx = 18Cx+2 ⟹ x + x + 2 = 18 2x + 2 = 18 2x = 18 - 2 = 16 2x = 16 x = 8 Combinations – Exercise – 17.1 – Q.7 If nCp = nCq The p + q = n ⟹ 15C3r = 15Cr+3 4r + 3 = 15 4r = 15 - 3 = 12 r = 3 Combinations – Exercise – 17.1 – Q.8 8Cr = 7C2 + 7C3 Applying formula Cancelling 7! from both sides Cancelling 8 on both sides 2 × 5 × 3 × 4 × 3 × 2 × 1 = r!(8 - r)! (3 × 2)(5 × 4 × 3 × 2 × 1) = r!(8 - r)! ⟹ r! = 3! r = 3 or r! = 5! r = 5 Combinations – Exercise – 17.1 – Q.9 80 - 5r = 11r 80 = 16r r = 80/16 r = 5 r = 5 Combinations – Exercise – 17.1 – Q.10 Cancelling (n - 2)! from numerator and denominator
= 5 + 10 +10 + 5 + 1
= 31
Hence n = n
r = 12 and 5
Applying formula
nCp = nCq = n
Then p + q = n
⟹ nC12 = nC5
12 + 5 = n
⟹ n = 17
If nCp = nCq
⟹ nC4 = nC6
4 + 6 = n
⟹ n = 10
then 12Cn = 12C10 Applying (i)
If nCp = nCp
The p + q = n
⟹ nC10 = nC12
10 + 12 = n
⟹ n = 22
Find 23Cn
⟹ 23C22
If nCp = nCr then P + r = n
∴ x + 2x + 3 = 24
3x = 21
x = 7
⟹ p + q = n
also Cx = 18Cx+2
⟹ x + x + 2 = 18
2x + 2 = 18
2x = 18 - 2 = 16
2x = 16
x = 8
⟹ 15C3r = 15Cr+3
4r + 3 = 15
4r = 15 - 3 = 12
r = 3
8Cr = 7C2 + 7C3
Cancelling 7! from both sides
Cancelling 8 on both sides
2 × 5 × 3 × 4 × 3 × 2 × 1 = r!(8 - r)!
(3 × 2)(5 × 4 × 3 × 2 × 1) = r!(8 - r)!
⟹ r! = 3!
or
r! = 5!
r = 5
80 - 5r = 11r
80 = 16r
r = 80/16
Cancelling (n - 2)! from numerator and denominator
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Chapter 17: Combinations – Exercise 17.3...
Chapter 17: Combinations – Exercise 17.2...
