Counting question (Source GMAT PREP)

[mach81]

Would appreciate if somebody could help me with these two COUNTING questions (I guess the factorial formaula can be used, but HOW?)

1) There are 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (Ans = 100)

2)All the stocks on the OTC are designated by either 4 letters OR a 5 letters code, using 26 letters of the alphabet. What are the maximum number of stocks that can be represented (And = 27((26)^4)

Thanks

[wizardofwashington]

Let us find how many 3-member teams can be formed from a total of 10 people (4+6). => 10 C3 = 120

Now, with the question statement "at least one senior partner must be present in these teams", we should calculate the # of possibilities without any senior partner (only juniors) and subtract this number from the 120 we calculated above.

# of possibilities without any senior partner = # of possibilities with only junior partners

Therefore, # of combinations of teams fully populated with Junior members - 6C3 = 20

So, the answer is 120-20 = 100.

[wizardofwashington]

2)All the stocks on the OTC are designated by either 4 letters OR a 5 letters code, using 26 letters of the alphabet. What are the maximum number of stocks that can be represented (And = 27((26)^4)

Question 2 has already been discussed on this forum. Please check the following link..

https://www.beatthegmat.com/viewtopic.php?p=19992#19992

[kajcha]

My approach for first question

Possible combinations SJJ, SSJ, SSS

4C1*6C2+4C2*6C1+4C3 = 100