Advertisements
Advertisements
प्रश्न
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
पर्याय
420
360
400
300
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate 4! – 3!
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all 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 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?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 5 different balls be distributed among three boxes?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Evaluate each of the following:
Evaluate each of the following:
6P6
The number of arrangements of the word "DELHI" in which E precedes I is
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 the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Evaluate the following.
`(3! + 1!)/(2^2!)`
The number of ways to arrange the letters of the word “CHEESE”:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
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?
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
