How many three-digit numbers are there, with distinct digits, wit… - Vidyadip

Question

How many three-digit numbers are there, with distinct digits, with each digit odd?

✓

Answer

The odd number digits are 1, 3, 5, 6, 9 Total number of odd digits = 5 $\therefore$ Required number of 3 digit num bars = number of arrangenments of 5 digits by taking 3 at a time $=\ ^{5}\text{P}_3$$=\frac{5!}{(5-3)!}$
$=\frac{5!}{2!}$
$=\frac{5\times4\times3\times2!}{2!}$
$=60$
Hence, total number of 3 digit numbers are 60.

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

Similar questions

Let $X=\{1,2,3,4\}$ and $Y=\{1,5,9,11,15,16\}$. Determine which of the following sets are functions from $X$ to $Y$ : $f_2=\{(1,1),(2,7),(3,5)\}$

Let A = {6, 8} and B = {1, 3, 5}. Show that R1 = {(a, b) / a ∈ A, b ∈ B, a – b is an even number} is a null relation, R2 = {(a, b) / a ∈ A, b ∈ B, a + b is an odd number} is a universal

If $\sin\alpha+\sin\beta=\text{a}$ and $\cos\alpha+\cos\beta=\text{b}$ prove that
$\cos(\alpha-\beta)=\frac{\text{a}^2+\text{b}^2-2}{2}$

$\frac{n^2-9}{(n+3) !}+\frac{6}{(n+2) !}-\frac{1}{(n+1) !}$

Find the angle between the X-axis and the line joining the points (3, -1) and (4, -2).

A man is employed to count ₹ 10710. he count at the rate od ₹ 180 per minute for half an hour. after this he counts at the rate of ₹ 3 less every minute than the preceding minute. find the time takan by him to count the entire amount.

if $5 \tan A=\sqrt{2}, \pi<A<\frac{3 \pi}{2}$ and $\sec B=\sqrt{11}, \frac{3 \pi}{2}<B<2 \pi$ then find the value of $\operatorname{cosec} A-\tan B$

$m$ men and $n$ women are to be seated in a row so that no two women sit together, if $m > n$ then show that the number of ways in which they can be seated as $\frac{\text{m}! (\text{m}+1)!(\text{m}−\text{n}+1)!}{\text{m}! (\text{m}+1)!(\text{m}-\text{n}+1) !}$

Find equations of lines which pass through the origin and make an angle of $45^{\circ}$ with the line $3 x-y=6$.

Find 2 × 5 × 8 + 4 × 7 × 10 + 6 × 9 × 12 + …… upto n terms.