00:01
In this problem, we have been asked to determine the given combinations n -cr.
00:06
Now, recall the formula for n -c -r, that is equal to n -factorial by r -factorial times the factorial of n -minus r.
00:16
So, let us do the first part.
00:18
The first sub -part is 10 -c -3.
00:22
So using this formula, that will be 10 -factorial by 3 -factorial times 10 - minus 3 -factorial.
00:31
So let us calculate this.
00:33
This is 10 factorial by 3 factorial times 7 factorial.
00:38
We can write 10 factorial as 10 times 9 times 8 times 7 factorial.
00:44
3 factorial is 3 times 2 times 1 and here we have 7 factorial.
00:49
We can cancel out these two 7 factorials and we are left with 10 times 9 times 8 divided by 3 times 2 times 1 and that is equal to 120.
00:58
So the first answer is 120.
01:02
Next, we need to determine 10c1.
01:07
So if we use that formula again, this is 10 factorial by 1 factorial times the factorial of 10 minus 1...