Advertisements
Advertisements
प्रश्न
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
Advertisements
उत्तर
All the vowels are together.
Take all the vowels as 1 unit.
Remaining consonants = 6
Total number of units for arrangement = 7
Number of arrangements = `(7!)/(2!)`
(Since in the consonant’s T’ s repeated twice)
= `(1 xx 2 xx 3 xx 4 xx 5 xx 6 xx 7)/(1 xx 2)`
= 2520
Among the vowels, the number of arrangements
= `(6!)/(2! xx 3!)`
= `(1 xx 2 xx 3 xx 4 xx 5xx 6)/(1 xx 2 xx 1 xx 2 xx 3)`
= 60
∴ Total number of arrangements = 2520 × 60
= 151200
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
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?
In how many ways can 4 letters be posted in 5 letter boxes?
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects 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
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
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
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
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?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
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 ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
