Advertisements
Advertisements
प्रश्न
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
Advertisements
उत्तर
Number of vowels = 2
Number of consonants = 5
Considering the two vowels as a single entity, we are now to arrange 6 entities taken all at a time.
Total number of ways = 6!
Also, the two vowels can be mutually arranged amongst themselves in 2! ways.
By fundamental principle of counting:
Total number of words that can be formed = 6!\[\times\]2! = 1440
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
If (n + 2)! = 60 [(n − 1)!], find n.
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
Prove that:
If P (5, r) = P (6, r − 1), find r ?
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If P (n, 5) = 20. P(n, 3), find n ?
If nP4 = 360, find the value of n.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?
Find the number of words formed by permuting all the letters of the following words:
INDIA
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.
If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?
In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:
the relative order of vowels and consonants do not alter?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
