If ^15 C_ 3r = ^15 C_ r+3 , Find r. - Vidyadip

Question

If ${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$ Find $r.$

✓

Answer

We have,
If $^nC_p =\ ^nC_q = n$
Then $p + q = n$
Also,
${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$
$\Rightarrow 3r + r + 3 = 15$
$4r + 3 = 15$
$4r = 15 - 3$
$4r = 12$
$r = 3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Binomial Theorem→Binomial Theorem — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the ratio in which the line Segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z =5.

Find the equation of the circle which circumscribes the triangle formed by the lines
$2x + y - 3 = 0, x + y - 1 = 0$ and $3x + 2y - 5 = 0$

Find the equation of the straight line passing through $(3, -2)$ and making an angle of $60^\circ $ with the positive direction of $y-$axis.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}(\cos\text{x}+\text{a}\sin\text{bx})^\frac{1}{\text{x}}$

Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.

Which of the following are ture.
(2 × 3)! = 2! × 3!

Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find:
$\text{B}\cap\text{C}$

If P and Q are two sets such that P has 40 elements, $\text{P}\cup\text{Q}$ has 60 elements and $\text{P}\cap\text{Q}$ has 10 elements, how many elements does Q have?

If $\text{f(x)}=\begin{cases}\text{x}^2,&\text{when }\text{ x}<0\\\text{x},&\text{when }\ 0\leq\text{x}<1\\\frac{1}{\text{x}},&\text{when }\text{ x}>0\end{cases}$
Find:

$\text{f}\Big(\frac{1}{2}\Big)$
$\text{f}(-2)$
$\text{f}(1)$
$\text{f}(\sqrt{3})$
$\text{f}(\sqrt{-3})$

If A and B are two set having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A × B) and $\text{n}\big[(\text{A}\times\text{B})\cap(\text{B}\times\text{A})\big]$