Advertisements
Advertisements
Question
Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2
Advertisements
Solution
For any n with r = 2
`("n"!)/("r"!("n" - "r")!)= ("n"!)/(2!("n" - 2)!)`
= `("n"("n" - 1)("n" - 2)!)/(1 xx 2 xx ("n" - 2)1)`
= `("n"("n" - 1))/2`
= `("n"^2 - "n")/2`
APPEARS IN
RELATED QUESTIONS
A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?
A teacher wants to select the class monitor in a class of 30 boys and 20 girls. In how many ways can the monitor be selected if the monitor must be a girl or a boy?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
A letter lock contains 3 rings, each ring containing 5 different letters. Determine the maximum number of false trials that can be made before the lock is opened?
A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?
How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?
A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?
How many strings can be formed using the letters of the word LOTUS if the word neither starts with L nor ends with S?
Find the value of 3! × 2!
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2
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?
Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.
The number of possible outcomes when a coin is tossed 6 times is ______.
The number of different four-digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is ______.
The number of six-digit numbers, all digits of which are odd is ______.
