Advertisements
Advertisements
Question
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Advertisements
Solution
`1/(6!) + 1/(7!) = x/(8!)`
⇒ `1/(6!) + 1/(7 xx 6!) = x/(8 xx 7 xx 6!)`
⇒ `1/(6!) (1 + 1/7) = x/(8 xx 7 xx 6!)`
⇒ `1 + 1/7 = x/(8 xx 7)`
⇒ `8/7 = x/(8 xx 7)`
⇒ x = `(8 xx 8 xx 7)/7`
∴ x = 64
APPEARS IN
RELATED QUESTIONS
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
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 of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
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?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Evaluate each of the following:
8P3
Evaluate each of the following:
Evaluate each of the following:
P(6, 4)
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
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
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
Find the rank of the word ‘CHAT’ in the dictionary.
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
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)`
Find the number of permutations of n different things taken r at a time such that two specific things 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
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, 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! |
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
