Question 1187675
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There are 10 pugs and 19 bulldogs. How many ways can we choose a team of 7 dogs 
if at least 1 team member needs to be a pug?
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<pre>
The total number of ALL possible combinations of 7 dogs taken at a time from 10+19 = 29 dogs is  

    {{{C[29]^7}}} = 1560780.


The number of all possible combinations of 7 buldogs taken at a time from 19 buldogs is

    {{{C[19]^7}}} = 50388.


To get the answer to the problem's question, subtract the second number from the first


    how many ways can we choose a team of 7 dogs  
    if at least 1 team member needs to be a pug  =  {{{C[29]^7}}} - {{{C[19]^7}}} = 1560780 - 50388 = 1510392.    <U>ANSWER</U>
</pre>

Solved.