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Applied Combinatorics: Inclusion-exclusion formula

Bruce Springsteen, aka The Boss, has just finished a large arena show. Since he has won $20$ Grammy Awards, he decides he will toss $20$ guitar picks into the crowd as souvenirs. He has a pile of $7$ identical red picks, $7$ identical yellow picks, $7$ identical gray picks, $7$ identical green picks, and $7$ […]