Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
The relative positions of all the vowels and consonants is fixed.
Arranging the six vowels at their places, without disturbing their respective places, we can arrange the six vowels in\[\frac{6!}{2!3!}\] ways.
Similarly, arranging the remaining 6 consonants at their places, without disturbing their respective places, we can arrange the 6 consonants in\[\frac{6!}{2!}\] ways.
By fundamental principle of counting, the number of words that can be formed =\[\frac{6!}{2!3!}\] X \[\frac{6!}{2!}\]= 21600
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
Prove that: n! (n + 2) = n! + (n + 1)!
Prove that:
Prove that:
If P (n, 5) = 20. P(n, 3), find n ?
If P (n, 4) = 12 . P (n, 2), find n.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
In how many ways can five children stand in a queue?
How many three-digit numbers are there, with no digit repeated?
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?
If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
How many permutations can be formed by the letters of the word, 'VOWELS', when
there is no restriction on letters?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all vowels come together?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
How many three letter words can be made using the letters of the word 'ORIENTAL'?
Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE
Find the number of words formed by permuting all the letters of the following words:
INDIA
Find the number of words formed by permuting all the letters of the following words:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
SERIES
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
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 ?
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
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used at a time
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
