Advertisements
Advertisements
प्रश्न
Find x in each of the following:
Advertisements
उत्तर
\[ \frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}\]
\[ \Rightarrow \frac{x}{10!} = \frac{1}{8!} + \frac{1}{9(8!)}\]
\[ \Rightarrow \frac{x}{10!} = \frac{9 + 1}{9(8!)} \]
\[ \Rightarrow \frac{x}{10!} = \frac{10}{9!}\]
\[ \Rightarrow \frac{x}{10 \times 9!} = \frac{10}{9!}\]
\[ \Rightarrow x = 100\]
APPEARS IN
संबंधित प्रश्न
Compute `(8!)/(6! xx 2!)`
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 4-digit numbers are there with no digit repeated?
Find r if `""^5P_r = ""^6P_(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?
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
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?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
The number of five-digit telephone numbers having at least one of their digits repeated 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
The number of ways to arrange the letters of the word CHEESE are
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
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?
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The total number of 9 digit number which has all different digit is:
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 each question has four choices?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur 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?
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
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 three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
