binomial iit 2000S
anyone has dare to solve it
Attachments:
Answers
Answered by
2
Answer:
(d) ⁵⁶c₄
Step-by-step explanation:
To find--->
-------------
6
⁵⁰C₄ + Σ ⁵⁶⁻ʳC₃
r=1
Solution--->
--------------
We have a formula
ⁿCᵣ+₁ + ⁿCᵣ = ⁿ⁺¹Cᵣ+ ₁
Applying this formula
Now
6
⁵⁰C₄ + Σ ⁵⁶ ⁻ ʳ C₃
r= 1
= ⁵⁰C₄ + ⁵⁶⁻¹C₃ + ⁵⁶⁻²C₃ + ⁵⁶⁻³C₃ + ⁵⁶⁻⁴C₃
+⁵⁶⁻⁵C₃ + ⁵⁶⁻⁶C₃
=(⁵⁰C₄ + ⁵⁰C₃) + ⁵¹C₃ + ⁵²C₃ +⁵³C₃ + ⁵⁴C₃
+⁵⁵C₃
=(⁵¹C₄ + ⁵¹C₃) + ⁵²C₃ + ⁵³C₃ + ⁵⁴C₃ +⁵⁵C₃
=( ⁵²C₄ + ⁵²C₃) + ⁵³C₃ + ⁵⁴C₃ +⁵⁵C₃
= (⁵³C₄ + ⁵³C₃) + ⁵⁴C₃ + ⁵⁵C₃
=( ⁵⁴C₄ + ⁵⁴C₃) +⁵⁵C₃
= ⁵⁵C₄ + ⁵⁵C₃
= ⁵⁶C₄
Similar questions