Advertisements
Advertisements
Question
Find the value of n if (n + 1)! = 20(n − 1)!
Advertisements
Solution
(n + 1)! = 20(n – 1)!
(n + 1) n(n – 1)! = 20(n – 1)!
n(n + 1) = 20
n2 + n – 20 = 0
n2 + 5n – 4n – 20 = 0
n(n + 5) – 4(n + 5) = 0
(n – 4)(n + 5) = 0
n – 4 = 0 or n + 5 = 0
n = 4 or n = – 5
But n = – 5 is not possible.
∴ n = 4
APPEARS IN
RELATED QUESTIONS
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many numbers between 100 and 1000 have 4 in the units place?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
Select the correct answer from the given alternatives.
A college offers 5 courses in the morning and 3 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening
Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?
A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?
Four children are running a race:
In how many ways can the first two places be filled?
Four children are running a race:
In how many different ways could they finish the race?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is allowed
How many numbers are there between 1 and 1000 (both inclusive) which are divisible neither by 2 nor by 5?
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Choose the correct alternative:
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is
Choose the correct alternative:
The number of 10 digit number that can be written by using the digits 2 and 3 is
How many numbers are there between 99 and 1000 having atleast one of their digits 7?
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.
The number of six-digit numbers, all digits of which are odd is ______.
