हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Evaluate nrnrn!r!(n-r)! when for any n with r = 2 - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2

योग

उत्तर

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`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Combinatorics and Mathematical Induction - Exercise 4.1 [पृष्ठ १६६]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 4 Combinatorics and Mathematical Induction
Exercise 4.1 | Q 15. (iii) | पृष्ठ १६६

संबंधित प्रश्न

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?


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?


How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?


How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?


How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?


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


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?


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?


How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are not allowed?


Find the value of 3! – 2!


Find the value of `(("n" + 3)!)/(("n" + 1)!)`


Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 6, r = 2


Choose the correct alternative:
The number of 5 digit numbers all digits of which are odd i


Choose the correct alternative:
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is


In a class, there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class for a function. In how many ways can the teacher make this selection?


In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.


There are four bus routes between A and B; and three bus routes between B and C. A man can travel round-trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, in how many ways can he make round trip?


In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answer correct is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×