Advertisements
Advertisements
प्रश्न
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?
उत्तर
Total number of words by taking 4 letters out of 6 at a time = `""^("6")"P"_4` = 6 x 5 x 4 x 3 = 360 whereas words can be with or without meaning.
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P (5, r) = P (6, r − 1), find r ?
If nP4 = 360, find the value of n.
If P (9, r) = 3024, find r.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
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?
Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
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 occupy only the odd places?
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?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
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:
RUSSIA
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
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?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
Find the total number of ways in which six '+' and four '−' signs can be arranged in a line such that no two '−' signs occur together.
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
Evaluate
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.