If ^16 C_ r = ^16 C_ r+2 , find ^7 C_ 4 . - Vidyadip

Question

If ${^\text{16}}\text{C}_{\text{r}}={^\text{16}}\text{C}_{\text{r+2}},$ find ${^\text{7}}\text{C}_{4}.$

✓

Answer

We have, If ${^\text{n}}\text{C}_{\text{r}}={^\text{n}}\text{C}_{\text{p}}$ then r + p = n 16 = r + r + 2 r = 7 then ${^\text{n}}\text{C}_{\text{4}}={^\text{7}}\text{C}_{\text{4}}$ $\Rightarrow \frac{7!}{4!(7-4)!}$ $\Rightarrow \frac{7\times5\times6}{3\times2}$ $\Rightarrow 35$

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 "(Each question 4 marks)" from Combinations→Combinations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{{\pi}}}\frac{1+\cos\text{x}}{\tan^2\text{ x}}$

The vertices of a triangle ABC are A(0, 0), B(2, -1) and C(9, 2). Find cos B.

If $2\tan\frac{\alpha}{2}=\tan\frac{\beta}{2},$ prove that $\cos\alpha=\frac{3+5\cos\beta}{5+3\cos\beta}$

Find the equation of the hyperbola whose,Focus is (2, 2) directrix is $\text{x+y}=\text{9}$ and eccentricity = 2

Differentiate the following from first principle:$\text{x}^3+4\text{x}^2+3\text{x}+2$

If a, b, c are in A.P.; b, c, d are in G.P. and $\frac { 1 } { c } , \frac { 1 } { d } , \frac { 1 } { e }$ are in A.P., prove that a, c, e are in G.P.

$\text{a}(\cos\text{B}\cos\text{C}+\cos\text{A})=\text{b}(\cos\text{C}\cos\text{A}+\cos\text{B})\\=\text{c}(\cos\text{A}\cos\text{B}+\cos\text{C}).$

From the prices of shares X and Y below, find out which is more stable in value:

X	35	54	52	53	56	58	52	50	51	49
Y	108	107	105	105	106	107	104	103	104	101

The upper part of a tree broken by the wind makes an angle of 30° with the ground and the distance from the root to the point where the top of the tree touches the ground is 15m. Using sine rule, find the height of the tree.

Evaluate: $\bigg[\text{i}^{18}+\Big(\frac{1}{\text{i}}\Big)^{25}\bigg]^{3}.$