n C T - n C r -1- n - r - rA- TrueB- False

The correct option is B False ^nC_r/^nC_r 1× r= n!/(n r)!× r!(r 1)!× (n r+1)!/n! =n r+1/r ...

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

Byju's Answer

Standard XI

Mathematics

Binomial Coefficients

n C T / n C r...

Question

$\frac{^{n} C_{r}}{^{n} C_{r - 1}} = \frac{n - r}{r}$

True

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

False

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

Open in App

Solution

The correct option is B
False

$\frac{^{n} C_{r}}{^{n} C_{r - 1}} \times r = \frac{n!}{(n - r)! \times r!} \frac{(r - 1)! \times (n - r + 1)!}{n!}$
$= \frac{n - r + 1}{r}$

Suggest Corrections

Similar questions

Let r and n be positive integers such that $1 \leq r \leq n .$ Then prove the following :

(i) $\frac{^{n} C_{r}}{^{n} C_{r - 1}} = \frac{n - r + 1}{r}$
(ii) $n^{n - 1} C_{r - 1} = (n - r + 1)^{n} C_{r - 1}$
(iii) $\frac{^{n} C_{r}}{^{n - 1} C_{r - 1}} = \frac{n}{r}$
(iv) $^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C_{r - 2} =^{n + 2} C_{r}$

Q. If

a_{n} = \sum_{r = 0}^{n} \frac{1}{^{n} C_{r}}

then

\sum_{r = 0}^{n} \frac{r}{^{n} C_{r}}

equals

If r is the inradius and R is the circumradius, then $2 R \leq r$

Q. If r is the radius and R is the circumradius. Then

2 R \leq r

$^{n + 1} C_{r + 1}$ = $\frac{n + 1}{r + 1}$ $^{n} C_{r}$

Join BYJU'S Learning Program

nCrnCr−1=n−rr

The correct option is B False nCrnCr−1×r=n!(n−r)!×r!(r−1)!×(n−r+1)!n! =n−r+1r

$\frac{^{n} C_{r}}{^{n} C_{r - 1}} = \frac{n - r}{r}$

The correct option is B
False

$\frac{^{n} C_{r}}{^{n} C_{r - 1}} \times r = \frac{n!}{(n - r)! \times r!} \frac{(r - 1)! \times (n - r + 1)!}{n!}$
$= \frac{n - r + 1}{r}$