Advertisements
Advertisements
प्रश्न
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Advertisements
उत्तर
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is 151200.
Explanation:
Total number of words is INTERMEDIATE = 12
Which have 6 vowels and 6 consonants
If two vowels never come together then we can arrange as under
V C V C V C V C V C V C V
Here, vowels are IEEIAE where 2 I’s and 3 E’s are there.
∴ Number of ways of arranging vowels = `(7!)/(3!2!)` = 420.
Consonants are NTRMDT where 2T’s are there
∴ Number of ways arranging consonants = `(6!)/(2!)`
= `(6*5*4*3*2!)/(21)` = 360
So, the total number of words are = 420 × 360
= 151200
Hence, the value of the filler is 151200.
APPEARS IN
संबंधित प्रश्न
Is 3! + 4! = 7!?
Compute `(8!)/(6! xx 2!)`
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = ""^6P_(r-1)`
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Which of the following are true:
(2 +3)! = 2! + 3!
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
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?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Evaluate each of the following:
Evaluate each of the following:
6P6
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
The number of arrangements of the word "DELHI" in which E precedes I is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
The total number of 9 digit number which has all different digit is:
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
