nCr +nCr–1=?
Explanation: 
Another Explanation (5):
আমরা জানি, nCr = \( \frac{n!}{r!(n-r)!} \)
তাহলে, nCr + nCr–1 = \( \frac{n!}{r!(n-r)!} + \frac{n!}{(r-1)!(n-r+1)!} \)
= \( \frac{n!}{(r-1)!(n-r)!} [\frac{1}{r} + \frac{1}{n-r+1}] \) 🤔
= \( \frac{n!}{(r-1)!(n-r)!} [\frac{n-r+1+r}{r(n-r+1)}] \) 🤓
= \( \frac{n!}{(r-1)!(n-r)!} [\frac{n+1}{r(n-r+1)}] \) 🤯
= \( \frac{(n+1)!}{r!(n-r+1)!} \) 🎉
= n+1Cr 😎
অতএব, nCr + nCr–1 = n+1Cr 🥳
