Advertisements
Advertisements
प्रश्न
if `1/(6!) + 1/(7!) = x/(8!)`, find x
उत्तर
`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
संबंधित प्रश्न
Is 3! + 4! = 7!?
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
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:
Which of the following are true:
(2 × 3)! = 2! × 3!
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?
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:
P(6, 4)
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, 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
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
If (n+2)! = 60[(n–1)!], find n
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?
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
If nP4 = 12(nP2), find n.
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 possible outcomes when a coin is tossed five times:
The number of ways to arrange the letters of the word “CHEESE”:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
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?
Find the distinct permutations of the letters of the word MISSISSIPPI?
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 the vowels and consonants are alternative
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
C1 | C2 |
(a) How many numbers are formed? | (i) 840 |
(b) How many number are exactly divisible by 2? | (i) 200 |
(c) How many numbers are exactly divisible by 25? | (iii) 360 |
(d) How many of these are exactly divisible by 4? | (iv) 40 |
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 ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.