Advertisements
Advertisements
प्रश्न
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
Advertisements
उत्तर
One million (1,000,000) consists of 7 digits.
We have digits 2, 3, 0, 3, 4, 2 and 3.
Numbers formed by arranging all these seven digits =\[\frac{7!}{2!3!}\]
But, these numbers also include the numbers whose first digit is 0.
This is invalid as in that case the number would be less than a million.
Total numbers in which the first digit is fixed as 0 = Permutations of the remaining 6 digits =\[\frac{6!}{2!3!}\]
Numbers that are greater than 1 million =\[\frac{7!}{2!3!}\] - \[\frac{6!}{2!3!}\]= 360
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
If P (n, 5) = 20. P(n, 3), find n ?
If P (n, 5) : P (n, 3) = 2 : 1, find n.
If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
In how many ways can five children stand in a queue?
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?
How many three-digit numbers are there, with no digit repeated?
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
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 'STRANGE' be arranged so that
the vowels come together?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
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 letter G always occupies the first place?
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?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with O and ends with L?
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?
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.
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:
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 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 permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
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?
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'?
Evaluate
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
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time
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 but first letter is a vowel?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
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 parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
