Ms. Granger has 24 cat figurines and 6 dog figurines in her drawer. in how many ways can a group of 6 figurines be chosen if there must be at least 4 cat figurines

There can be 3 cases:

Case 1: There are 4 cat figurines

Total no of ways=^{24}C_{4}*^{6}C_{2}

=10626*15=159390

Case 2: There are 5 cat figurines

Total no of ways=^{24}C_{5}*^{6}C_{1}

=42504*6=255024

Case 3: There are 6 cat figurines

Total no of ways=^{24}C_{6}*^{6}C_{0}

=134596

Total no of ways=Sum of all cases

=134596+255024+159390=549010 ways

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