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 "3 Marks Question" from Permutations→Permutations — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

There are 10 persons named P₁ , P₂ , P₃ , ... P_10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P₁must occur whereas P₄ and P₅ do not occur. Find the number of such possible arrangements.
[Hint: Required number of arrangement = ⁷C₄ × 5!]

Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

If a and b are distinct integers, prove that a - b is a factor of aⁿ - bⁿ, whenever n is a positive integer.
[Hint write aⁿ = (a – b + b)ⁿ and expand]

Evaluate the following:

$(\sqrt3+1)^5-(\sqrt3-1)^5$

Show that the products of the corresponding terms of the sequences a, ar, ar² ,........arⁿ^-1 and A, AR, AR²......AR^n-1form a G.P. and find the common ratio.

If $\text{f(x)}=(\text{a}-\text{x}^\text{n})^{\frac{1}{\text{n}}},\text{a}>0$ and $\text{n}\in\text{N},$ then prove that f(f(x)) = x for all x.

Find the sum of the following series:
5 + 55 + 555 + ... to n terms.

Differentiate the following functions with respect to x:

$\frac{\text{x}}{1+\tan\text{x}}$

The letters of the word SURITI are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word SURITI.

Prove that: $\sin^2\text{(n+1)}\text{A}-\sin^2\text{nA}=\sin\text{(2n+1)}\text{A}\sin\text{A}$