Question

For a fishing trip, Abdul is going to choose lures to put in his tackle box. He has 6 lures that are buzzbaits and 9 that are crankbaits. In how many ways can he choose 5 lures if fewer than 3 must be crankbaits?

a) 84

b) 126

c) 56

d) 42

Answer 1

Abdul can choose 5 lures with fewer than 3 crankbaits in 130 ways.

Step-by-step explanation:

To find the number of ways Abdul can choose 5 lures with fewer than 3 crankbaits, we can use combinatorics. If we choose 0 crankbaits, we must choose all 5 lures from the 6 buzzbaits. This can be done in 6 choose 5 or 6 ways.

If we choose 1 crankbait, we must choose 4 more lures from the remaining 5 buzzbaits and 8 crankbaits. This can be done in (5 choose 4) * (8 choose 1) or 40 ways.

Lastly, if we choose 2 crankbaits, we must choose 3 more lures from the remaining 4 buzzbaits and 7 crankbaits. This can be done in (4 choose 3) * (7 choose 2) or 84 ways. Summing up the three cases, the total number of ways is 6 + 40 + 84 = 130 ways.