Advertisements
Advertisements
Question
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
Options
420
360
400
300
Advertisements
Solution
360
10 lakhs consists of seven digits.
Number of arrangements of seven numbers of which 2 are similar of first kind, 3 are similar of second kind =\[\frac{7!}{2!3!}\]
But, these numbers also include the numbers in which the first digit has been considered as 0. This will result in a number less than 10 lakhs. Thus, we need to subtract all those numbers.
Numbers in which the first digit is fixed as 0 = Number of arrangements of the remaining 6 digits =\[\frac{6!}{2!3!}\]
Total numbers greater than 10 lakhs that can be formed using the given digits =\[\frac{7!}{2!3!}\] -\[\frac{6!}{2!3!}\]
420-60
= 360
APPEARS IN
RELATED QUESTIONS
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Find r if `""^5P_r = 2^6 P_(r-1)`
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Find x in each of the following:
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
Find x if `1/(6!) + 1/(7!) = x/(8!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Find the distinct permutations of the letters of the word MISSISSIPPI?
How many ways can the product a2 b3 c4 be expressed without exponents?
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
