मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता 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

बेरीज
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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Combinatorics and Mathematical Induction - Exercise 4.1 [पृष्ठ १६६]

APPEARS IN

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

संबंधित प्रश्‍न

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?


How many two-letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?


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


How many two letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?


If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?


How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?


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


A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?


How many three-digit numbers are there with 3 in the unit place? 
without repetition


How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed


Count the numbers between 999 and 10000 subject to the condition that there are at least one of the digits is repeated


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 4! + 5!


Find the value of 3! × 2!


Find the value of n if (n + 1)! = 20(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


In a steamer there are stalls for 12 animals, and there are horses, cows and calves (not less than 12 each) ready to be shipped. They can be loaded in 312 ways.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×