Welcome to the NCERT Solutions for Class 11th Mathematics - Chapter Permutations & Combinations. This page offers a step-by-step solution to the specific question from Exercise 1, Question 3: **how many 4 letter code can be formed using the fir...**.

Question 3

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Answer

There are as many codes as there are ways of filling 4 vacant places

in succession by the first 10 letters of the English alphabet, keeping in mind that the repetition of letters is not allowed.

The first place can be filled in 10 different ways by any of the first 10 letters of the English alphabet following which, the second place can be filled in by any of the remaining letters in 9 different ways. The third place can be filled in by any of the remaining 8 letters in 8 different ways and the fourth place can be filled in by any of the remaining 7 letters in 7 different ways.

Therefore, by multiplication principle, the required numbers of ways in which 4 vacant places can be filled is 10 × 9 × 8 × 7 = 5040

Hence, 5040 four-letter codes can be formed using the first 10 letters of the English alphabet, if no letter is 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 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

- 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?

- 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 a
_{n}=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?

- Q:-
Find the sum to

*n*terms of the sequence, 8, 88, 888, 8888… - Q:-
Solve 24x < 100, when

(i) x is a natural number. (ii) x is an integer. - Q:-
Find the sum to

*n*terms of the series 3 × 1^{2}+ 5 × 2^{2}+ 7 × 3^{2}+ … - Q:-
Find the sum to

*n*terms of the series whose*n*th term is given by*n*(*n*+ 1) (*n*+ 4). - Q:-
A point is on the

*x*-axis. What are its*y*-coordinates and*z*-coordinates? - 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:-
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:-
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:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- Q:-
Find the sum to

*n*terms in the geometric progression

Ayush
2018-09-19 21:23:11

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