Question

Find r, if $\rm ^{15}C_{4}+\ ^{15}C_{5}+\ ^{16}C_{6}+\ ^{17}C_{7} = \ ^{18}C_{r}$

Answer 1

Answer:

7 or 11

Step-by-step explanation:

Hi,

We know that ⁿCₓ₋₁ + ⁿCx = ⁿ⁺¹Cₓ,

¹⁵C₄ + ¹⁵C₅+ ¹⁶C₆ + ¹⁷C₇ = ¹⁸Cr ,

¹⁶C₅ + ¹⁶C₆ + ¹⁷C₇ = ¹⁸Cr

¹⁷C₆  + ¹⁷C₇ = ¹⁸Cr

¹⁸C₇  = ¹⁸Cr,

Also, if ⁿCr = ⁿCs , then either r = s or n = r + s

Hence , r = 7 or r + 7 = 18

r = 11.

Hence values of r are 7 or 11

Hope, it helps !