Advertisements
Advertisements
Question
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
Advertisements
Solution
The word INTERMEDIATE consists of 12 letters that include two Is, two Ts and three Es.
There are 6 vowels (I, I, E, E, E and A) that are to be arranged in six even places =\[\frac{6!}{2!3!}\]= 60
The remaining 6 consonants can be arranged amongst themselves in\[\frac{6!}{2!}\]
ways, which is equal to 360.
By fundamental principle of counting, the number of words that can be formed = 60\[\times\]360 = 21600
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
Prove that:
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P (n, 5) : P (n, 3) = 2 : 1, find n.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
In how many ways can five children stand in a queue?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
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?
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
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 different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letters P and I respectively occupy first and last place?
m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]
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 all letters are used but first is vowel.
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:
ARRANGE
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:
EXERCISES
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
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 different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?
In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?
The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Write the number of diagonals of an n-sided polygon.
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
