How many ways can a teacher arrange 10 students in a front row if there are 60 students
I think I do 60!/50! = 2.74 *10^17
How many ways can you choose committee of 7 from a total of 20
(20 nCr7) = 77520
Both correct!
Order is important for the first one, and not on the second.
To calculate the number of ways a teacher can arrange 10 students in a front row out of a total of 60 students, you would use the concept of permutations.
The number of permutations of selecting 10 students out of a total of 60 can be calculated using the formula for combinations, denoted as "nCr". The formula for combinations is:
nCr = n! / (r!(n-r)!),
where n is the total number of items and r is the number of items being chosen.
In this case, you would calculate 60C10 (60 choose 10). Plugging in the values into the formula:
60C10 = 60! / (10!(60-10)!)
= 60! / (10!50!)
= 60 x 59 x 58 x ... x 51 / 10 x 9 x 8 x ... x 2 x 1.
After simplifying the expression and canceling out common factors, you would get the result of approximately 2.74 x 10^17.
So, your calculation of 60!/50! is correct.
Regarding the second question, to find the number of ways you can choose a committee of 7 out of a total of 20 members, you would use the formula for combinations (nCr).
So, the number of ways to choose a committee of 7 out of 20 can be calculated as:
20C7 = 20! / (7!(20-7)!)
= 20! / (7!13!)
= 20 x 19 x 18 x ... x 14 / 7 x 6 x 5 x ... x 2 x 1.
After simplifying the expression, you would get the result of 77,520. Thus, your calculation of 20C7 is correct.