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

ⁿC_p = ⁿC_q = n

Then p + q = n

⟹ ⁿC₁₂ = ⁿC₅

12 + 5 = n

⟹ n = 17

 

Combinations – Exercise – 17.1 – Q.3

If  ⁿC_p = ⁿC_q

Then p + q = n

⟹ ⁿC₄ = ⁿC₆

4 + 6 = n

⟹ n = 10

then ¹²C_n = ¹²C₁₀
Applying (i)

 

Combinations – Exercise – 17.1 – Q.4

If ⁿC_p  = ⁿC_p

The p + q = n

⟹ ⁿC₁₀ = ⁿC₁₂

10 + 12 = n

⟹ n = 22

Find ²³C_n

⟹ ²³C₂₂