Question

A bag contains four red marbles, two green ones, one lavender one, three yellows, and three orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?

Answer 1

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Answer:

At most one yellow means => 1 or 0 yellow

1 yellow => 3C1*10C4 ( one yellow from three choices and 4 marbles from 10 non-yellow marbles)

=> 630

0 yellow => 10C5 => 5 marbles from 10 non-yellow marbles

=> 252

Total sets = 630 + 252 = 882 sets

A permutation of n items taken r at a time is an ORDERED LIST of r items chosen from n, P(n,r) = in-r)! A combination of n items taken r at a time is an UNORDERED SET of r items chosen from n, C(n,r) = r!(n-r)! Reminder: "alternatives" lead to addition principle, "sequence of steps" to multiplication principle