Class 11 Mathematics - Chapter Permutations & Combinations NCERT Solutions | How many 3-digit even numbers can be for
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
There will be as many ways as there are ways of filling 3 vacant places
in succession by the given six digits. In this case, the units place can be filled by 2 or 4 or 6 only i.e., the units place can be filled in 3 ways. The tens place can be filled by any of the 6 digits in 6 different ways and also the hundreds place can be filled by any of the 6 digits in 6 different ways, as the digits can be repeated.
Therefore, by multiplication principle, the required number of three digit even numbers is 3 × 6 × 6 = 108
More Questions From Class 11 Mathematics - Chapter Permutations & Combinations
- Q:-
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
- Q:-
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?
- Q:-
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
- Q:-
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
- Q:-
How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?
Popular Questions of Class 11 Mathematics
- Q:-
Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer. - Q:-
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
- Q:-
A point is on the x-axis. What are its y-coordinates and z-coordinates?
- Q:-
Find the equation of the circle with centre (0, 2) and radius 2
- Q:-
Describe the sample space for the indicated experiment: A coin is tossed three times.
- Q:-
Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.
- Q:- Write the first five terms of the sequences whose nth term is an=n(n+2)
- Q:-
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).
- Q:-
The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
- Q:-
A point is in the XZ-plane. What can you say about its y-coordinate?
Recently Viewed Questions of Class 11 Mathematics
- Q:-
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
- Q:-
- Q:-
If f is a function satisfying f(x +y) = f(x) f(y) for all x,y
N such that f(1) = 3
and , find the value of n. - Q:-
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
- Q:-
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
- Q:-
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
- Q:-
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
- Q:-
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
- Q:-
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
- All Chapters Of Class 11 Mathematics
- All Subjects Of Class 11