Advertisements
Advertisements
प्रश्न
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
Advertisements
उत्तर
Numbers greater than a million can be formed when the first digit can be any one out of the given digits 1, 2, 0, 2, 4, 2, 4, except 0.
Number of arrangements of the given digits 1, 2, 0, 2, 4, 2, 4 = Arrangements of 7 things of which 3 are similar to the first kind, and 2 are similar to the second kind =\[\frac{7!}{2!3!}\]
But, these arrangements also include the numbers in which the first digit is zero. This will make the number less than a million. So, it needs to be subtracted.
Number where the first digit is zero = Number of arrangements of the remaining 6 digits 1, 2, 2, 4, 2, 4 =\[\frac{6!}{2!3!}\]
Numbers greater than 1 million =\[\frac{7!}{2!3!}\]-\[\frac{6!}{2!3!}\]= 360
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
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 P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
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 from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?
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:
INDEPENDENCE
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:
PAKISTAN
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
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 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?
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'.
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 ?
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'?
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
If 35Cn +7 = 35C4n − 2 , then write the values of n.
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
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.
