Your office has arranged for a box of food packets conting2 pack
ets of noodles Jackets 3 of pasta and 4 packets of sushi
In how many ways can you pick 3 food pockets from the box so that least one of them contains pasta?
Answers
Given:
Number of packets of noodles = 2
Number of packets of pasta = 3
Number of packets of sushi = 4
To find:
Number of ways of picking 3 food packets so that at least one of them contains pasta.
Solution:
The number of possibilities will be:
- 1 pasta packet and 2 non pasta packet = 3C1 × 6C2
- 2 pasta packet and 1 non pasta packet = 3C2 × 6C1
- 3 pasta packet = 3C3
The total number of possibilities will be:
= 3C1 × 6C2 + 3C2 × 6C1 + 3C3
= 3 × 15 + 3 × 6 + 1
= 45 + 18 + 1
= 64
Thus the number of required possibilities is 64.
Given : food packets containing
2 packet noodles
3 packets pasta
4 packets Sushi
To Find : ways to pick 3 food pockets from the box so that atleast one of them contains pasta
Solution:
In addition to other answer , this is different way to get number of ways
2 packet noodles
3 packets pasta
4 packets Sushi
Total = 9
Ways to pick 3 packets out of 9 = ⁹C₃ = 84
atleast one of them contains pasta = Total ways - ways 0 pasta
0 pasta means 3 packets out of remaining 6 = ⁶C₃ = 20 ways
Hence ways to pick 3 food pockets from the box so that atleast one of them contains pasta = 84 - 20 = 64 ways
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