Find the value of: ^ 20 C_ 16 - ^ 19 C_ 16 - Vidyadip

Question

Find the value of: ${ }^{20} \mathrm{C}_{16}-{ }^{19} \mathrm{C}_{16}$

✓

Answer

$
\begin{aligned}
{ }^{20} \mathrm{C}_{16}-{ }^{19} \mathrm{C}_{16} & =\frac{20 !}{16 ! 4 !}-\frac{19 !}{16 ! 3 !} \\
& =\frac{20 \times 19 !}{16 ! \times 4 \times 3 !}-\frac{19 !}{16 ! 3 !} \\
& =\frac{19 !}{3 ! 16 !}\left[\frac{20}{4}-1\right] \\
& =\frac{19 !}{3 ! 16 !}(4) \\
& =\frac{19 !}{3 !(16)(15 !)} 4 \\
& =\frac{19 !}{4(3 !)(15 !)} \\
& =\frac{19 !}{4 ! 15 !} \\
& ={ }^{19} \mathrm{C}_{15} \text { or }{ }^{19} \mathrm{C}_4=3876
\end{aligned}
$

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.(1 Marks)" from Permutations and Combinations (p-2)→Permutations and Combinations (p-2) — all question types→Maths (commerce) STD 11 Commerce / Arts question papers→Maharashtra Board STD 11 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

If A = {1, 2, 3} and B = {2, 4}, state the elements of A × A, A × B, B × A, B × B, (A × B) ∩ (B × A).

Sudhakar invests ₹ 1344 in buying shares of face value $₹ 24$ selling at a $12 \%$ premium. The dividend on the shares is $15 \%$ per annum. Calculate: The dividend he receives annually.

Find the $x$ and $y$-intercepts of the following lines: $\frac{x}{3}+\frac{y}{2}=1$

A dividend of $9 \%$ was declared on $₹ 100$ shares selling at a certain price in the stock market. If the rate of return is $7.5 \%$ calculate: The amount to be invested to obtain an annual dividend of ₹ 630 .

Find $n$, if: $\frac{(17-n) !}{(14-n) !}=5$ !

From a group of 8 boys and 5 girls, a committee of five is to be formed. Find the probability that the committee contains: at least 3 boys.

A coin is tossed 8 times. In how many ways can we obtain: 4 heads and 4 tails?

Find the derivatives of the following functions w.r.t. x.
$x^{-9}$

Simplify the following and express in the form $a+i b$ : $3+\sqrt{ -64}$

Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangements where two specified delegates are: always together.