Advertisements
Advertisements
प्रश्न
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
Advertisements
उत्तर
In the word EQUATION, there are 5 vowels, namely, A, E, I, O, and U, and 3 consonants, namely, Q, T, and N.
Sequence of vowel letters = 5! = 5 x 4 x 3 x 2 x 1 = 120
Sequence of consonant letters = 3! = 3 x 2 x 1 = 6
Vowels and letters can be written in 2 ways, take vowels first or take consonants.
Words formed from the letters of the word EQUATION when vowels and consonants come together
120 x 6 x 2 = 1440
APPEARS IN
संबंधित प्रश्न
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
Compute:
Compute:
L.C.M. (6!, 7!, 8!)
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many 9-digit numbers of different digits can be formed?
Evaluate the following:
14C3
Evaluate the following:
12C10
Evaluate the following:
n + 1Cn
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl?
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
If 15C3r = 15Cr + 3 , then r is equal to
If nCr + nCr + 1 = n + 1Cx , then x =
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
If nC12 = nC8, then n is equal to ______.
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
