00:01
So we have to solve it is given if p n5 is equal to 1 .20 times c n3, then we have to find the value of n.
00:17
Now first write the definition of a p nr, which is given by n factorial by n minus r factorial and c n r is defined.
00:32
N factorial by r factorial into n minus r factorial now we have r are given only n is not available so c n 5 here becomes n b .m .5.
00:49
Factorial, which is equal to 120 times n factorial by nc3.
00:56
Cn3 means n factorial by 3 factorial into n minus 3 factorial.
01:03
We can cancel n factorial and factorial from both sides.
01:08
Then, taking this n minus 3 to this set, we have n minus 3 factorial by n minus 3 factorial by n minus 5 factorial is equal to 120 by 3 factorial is 6 which is equal to 20.
01:24
Now this n minus 3 factorial can be further defined by, since we know that n factorial is equal to n minus 1 into n minus 2 into extra up to 1.
01:37
Using that, we can split this n -3 factorial as n -minus 3 into n -3 minus -1, which is n -4 -1, which is n -5.
01:52
We can stop here since we wanted to cancel this n -5 factorial from the denominator.
01:59
So this will become like this, this is equal to 20...