Find the differences between the largest values in the following:…

Question

Find the differences between the largest values in the following: ${ }^{15} C_r-{ }^{11} C_r$

✓

Answer

Greatest value of ${ }^{15} \mathrm{C}_{\mathrm{r}}$
Here $\mathrm{n}=15$, which is odd
Greatest value of ${ }^n C_r$ occurs at $r=\frac{n-1}{2}$ if $n$ is odd
$
\begin{array}{ll}
\therefore & \mathrm{r}=\frac{\mathrm{n}-1}{2} \\
\therefore & \mathrm{r}=\frac{15-1}{2}=7
\end{array}
$
$\therefore \quad$ Greatest value of ${ }^{15} \mathrm{C}_{\mathrm{r}}={ }^{15} \mathrm{C}_7=\frac{15 !}{7 ! 8 !}$
$
=\frac{15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 !}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 8 !}
$
$=6435$
Also, for greatest value of ${ }^{11} \mathrm{C}_{\mathrm{r}}$ $\mathrm{n}=11$, which is odd
$
\begin{aligned}
\therefore \quad \mathrm{r}=\frac{11-1}{2} & =5 \\
\therefore \quad{ }^{11} \mathrm{C}_5 & =\frac{11 !}{5 ! 6 !} \\
& =\frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 !}{5 \times 4 \times 3 \times 2 \times 1 \times 6 !} \\
& =462
\end{aligned}
$
Difference between the greatest values of ${ }^{15} C_r$ and ${ }^{11} C_r=6435-462=5973$Find the differences between the largest values in the following: ${ }^{15} C_r-{ }^{11} C_r$

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 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

Solve the following quadratic equations.
$x^2-4 x+13=0$

→

Find the differences between the largest values in the following: ${ }^{13} \mathrm{C}_{\mathrm{r}}-{ }^8 \mathrm{C}_{\mathrm{r}}$

→

If the origin is shifted to the point O'(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the points (a) A(1, 3) (b) B(2, 5)

→

Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys and 1 girl and 3 boys. One child is selected at random from each group. What is the chance that the three selected consist of 1 girl and 2 boys?

→

Find the square roots of : 3 – 4i

→

Following data gives the coded price (X) and demand (Y) of a commodity.

Price	5	7	9	8	10	7	9	8	5	11	11	10	2	3	9
Demand	9	15	13	15	14	10	11	14	10	14	6	14	15	11	12
Price	2	4	3	14	6	10	7	15	8	6	5	6	11	14	15
Demand	6	11	8	11	10	15	9	15	13	9	14	10	7	5	6

Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y.
Also find
(i) marginal frequency distribution of X and Y.
(ii) conditional frequency distribution of Y when X is less than 10.

→

Find the nth terms of the sequences: 0.2, 0.22, 0.222,…..

→

Find the square roots of : 2 + 2√3i

→

The following data gives the age of 100 students in a school. Calculate variance and S.D.

Age (In years)	10	11	12	13	14
No. of Students	10	20	40	20	10

→

Find compound interest on $₹ 10,000$ for 2 years at $8 \%$ per annum compounded half yearly.

→

Permutations and Combinations (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

Answer

Need a full question paper?

Explore more

Similar questions