हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

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

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

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

How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?


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?


How many numbers between 100 and 1000 have 4 in the units place?


How many numbers between 100 and 1000 have the digit 7 exactly once?


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?


How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?


How many words can be formed by writing letters in the word CROWN in different order?


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.


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 numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if repetition of digits allowed


How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is allowed


Count the total number of ways of answering 6 objective type questions, each question having 4 choices


Find the value of 6!


Choose the correct alternative:
The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is


All the letters of the word PADMAPRIYA are placed at random in a row. The probability that the word PRIY A occurs without getting split is ______


How many numbers are there between 99 and 1000 having 7 in the units place?


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×