Advertisements
Advertisements
Question
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Solution
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
RELATED QUESTIONS
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of arrangements of the word "DELHI" in which E precedes I is
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The product of r consecutive positive integers is divisible by
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
Evaluate the following.
`(3! + 1!)/(2^2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
