
How do you evaluate
Answer
480k+ views
Hint: First of all, we have to address the formula and the values, then substitute the value of ‘n’ and ‘r’ in the formula and then find factorial for substituting values and then simply the expression.
Complete step by step solution:
We have been given that we have to find all the possible combinations for . So first we will address the formula, input parameters, and values in the formula.
Then substitute the values of ‘n’ and ‘r’ in the formula and then we have to find the factorial for substituting values, then substitute the corresponding value in the formula.
According to the question:
Given that,
n= 6 and r= 4
so, the formula is,
Now, we have to substitute ‘n’ and ‘r’ values in the formula,
Solving the above expression, we get –
Now, we have to find the factorial for , , and ,
So, substitute the corresponding value in the above expression,
Now, we have to simply the above expression, we get –
Again, solving the above expression, we get –
Now, we can clearly see that 30 and 2 have the same common, so they can easily cancel out.
So, 15 is the total possible combination for 6 CHOOSE 4
Hence, our required answer is 15.
Note:
In the case of combination, there is no order required but in permutation, the order is more important.
The product of all positive integers less than or equal to a given positive integer and denoted by the integer and an exclamation point. Thus factorial three is written , meaning . The factorial of zero is defined as equal to one, .
Complete step by step solution:
We have been given that we have to find all the possible combinations for
Then substitute the values of ‘n’ and ‘r’ in the formula and then we have to find the factorial for substituting values, then substitute the corresponding value in the formula.
According to the question:
Given that,
n= 6 and r= 4
so, the formula is,
Now, we have to substitute ‘n’ and ‘r’ values in the formula,
Solving the above expression, we get –
Now, we have to find the factorial for
So, substitute the corresponding value in the above expression,
Now, we have to simply the above expression, we get –
Again, solving the above expression, we get –
Now, we can clearly see that 30 and 2 have the same common, so they can easily cancel out.
So, 15 is the total possible combination for 6 CHOOSE 4
Hence, our required answer is 15.
Note:
In the case of combination, there is no order required but in permutation, the order is more important.
The product of all positive integers less than or equal to a given positive integer and denoted by the integer and an exclamation point. Thus factorial three is written
Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹37,300 per year
EMI starts from ₹3,108.34 per month
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
The flightless birds Rhea Kiwi and Emu respectively class 11 biology CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Whales are warmblooded animals which live in cold seas class 11 biology CBSE

Where can free central placentation be seen class 11 biology CBSE

What is the chemical name of Iron class 11 chemistry CBSE
