Download App

Permutations and Combination — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsPermutations and Combination3 Marks
Question
A code word is formed by two different English letters followed by two non-zero distinct digits. Find the number of such code words. Also, find the number of such code words that end with an even digit.
✓

Answer

There is a total of 26 alphabets. A code word contains 2 English alphabets.$\therefore 2$ alphabets can be filled in ${ }^{26} P _2$
$=\frac{26 !}{(26-2) !}$
$=\frac{26 \times 25 \times 24 !}{24 !}$
$=650 \text { ways. }$
Also, alphabets to be followed by two distinct non-zero digits from 1 to 9 which can be filled in
${ }^9 P_2=\frac{9 !}{(9-2) !}=\frac{9 \times 8 \times 7 !}{7 !}=72$ ways.
∴ Total number of a code words = 650 × 72 = 46800. To find the number of codewords end with an even integer. 2 alphabets can be filled in 650 ways. The digit in the unit’s place should be an even number between 1 to 9, which can be filled in 4 ways. Also, 10’s place can be filled in 8 ways. ∴ Total number of codewords = 650 × 4 × 8 = 20800

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 Combination→Permutations and Combination — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
→
If $a, b, c$ are in G.P. and $a x^2+2 b x+c=0$ and $p x^2+2 q x+r=0$ have common roots, then

verify that $p^2-2 q b a+r a^2=0$.

→
Find the sum of $n$ terms of the A.P. whose $k^{th} $ terms is $5k + 1.$
→
Find the equations of the tangents to the parabola $y^2=9 x$ through the point $(4,10)$.
→
Prove that $\cos ^2 x+\cos ^2\left(x+\frac{\pi}{3}\right)+\cos ^2\left(x-\frac{\pi}{3}\right)=\frac{3}{2}$
→
Prove that:
$\cos^3\text{x}\sin3\text{x}+\sin^3\text{x}\cos3\text{x}=\frac{3}{4}\sin4\text{x}$
→
If $\text{f(x)}=\text{x}^3-\frac{1}{\text{x}^3},$ show that $\text{f(x)}+\text{f}\Big(\frac{1}{\text{x}}\Big)=0$
→
Write the following relation as the sets of ordered pairs:
A relation R on the set {1, 2, 3, 4, 5, 6, 7}defined by $(\text{x, y})\in \text{R}\Leftrightarrow\text{x}$ is relatively prime to y.
→
Find the equation of the tangent to the hyperbola.: $3 x^2-y^2=12$ at the point $(4,6)$
→
$\sin \frac{\pi^c}{8}=\frac{1}{2} \sqrt{2-\sqrt{2}}$
→