Advertisements
Advertisements
Question
Find x in each of the following:
Advertisements
Solution
\[\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}\]
\[ \Rightarrow \frac{1}{6!} + \frac{1}{7(6!)} = \frac{x}{8!}\]
\[ \Rightarrow \frac{7 + 1}{7(6!)} = \frac{x}{8!}\]
\[ \Rightarrow \frac{8}{7!} = \frac{x}{8!}\]
\[ \Rightarrow \frac{8}{7!} = \frac{x}{8 \times 7!}\]
\[ \Rightarrow x = 64\]
APPEARS IN
RELATED QUESTIONS
Is 3! + 4! = 7!?
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
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 ?
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, 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
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
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?
If nP4 = 12(nP2), find n.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
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?
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 all the 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 0, 2, 5, 7, 8 without repetition?
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
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 ______.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
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 |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
