If m and n are positive integers- then value of m C 0 n C k - m C 1 n C k -1- m C k n C 0A - m - n C m - kB- m-n CkC- m-n Cn-kD- None of these

The correct option is B ^m+nC_kUsing Binomial theorem, ^m+nC_k=^mC_0^nC_k+^mC_1^nC_k 1+....+^mC_k^nC_0 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sequence

If m and n ar...

Question

If $m$ and $n$ are positive integers, then value of
$^{m} C_{0}^{n} C_{k} +^{m} C_{1}^{n} C_{k - 1} + . . . . +^{m} C_{k}^{n} C_{0}$

^{m + n} C_{k}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

^{m + n} C_{m + k}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

^{m + n} C_{n + k}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

Suggest Corrections

Similar questions

det ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} n \sum k = 0 k & n \sum k = 0^{n} C_{k} k^{2} n \sum k = 0^{n} C_{k} k & n \sum k = 0^{n} C_{k} 3^{k} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ = 0

n . Then n \sum k = 0 \frac{^{n} C_{k}}{k + 1}

n

C_{k} =^{n} C_{k},

n \sum k = 1 k^{3} {(\frac{C_{k}}{C_{k - 1}})}^{2}

(w i t h n \geq m)

(\begin{matrix} n m \end{matrix}) =^{n} C_{m}

(\begin{matrix} n m \end{matrix}) + (\begin{matrix} n - 1 m \end{matrix}) + (\begin{matrix} n - 2 m \end{matrix}) + . . . . . . . . . . + (\begin{matrix} m m \end{matrix}) = (\begin{matrix} n + 1 m + 1 \end{matrix})

^{50} C_{0} +^{51} C_{1} +^{52} C_{2} + . . . . . +^{100} C_{50} =^{n} C_{k}

n + k

^{50} C_{0} +^{51} C_{1} +^{52} C_{2} + . . . . . +^{100} C_{50} =^{n} C_{k}

n + k

Join BYJU'S Learning Program