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 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 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not 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 three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?


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?


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.


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?
with repetition


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


How many strings can be formed using the letters of the word LOTUS if the word neither starts with L nor ends with S?


In how many ways 10 pigeons can be placed in 3 different pigeon holes?


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


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


The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is ______.


The number of six-digit numbers, all digits of which are odd is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×