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Sagot :
Answer:
a) 4060 different combinations
b) 30!
Explanation:Given:
Total balls of different patterns = 30
To find:
a) the different three-ball combinations one can have if 3 balls are pulled out of the bag
b) the total number of possible combinations there are if you draw all the balls out of the bag one at a time in factorial form
a) To determine the 3-ball combinations, we will apply combination as the order they are picked doesnot matter
[tex]\begin{gathered} for^^^\text{ the 3 ball comination = }^nC_r \\ where\text{ n = 30, r = 3} \\ \\ ^{30}C_3\text{ = }\frac{30!}{(30-3)!3!} \\ ^{30}C_3\text{ = }\frac{30!}{27!3!}\text{= }\frac{30\times29\times28\times27!}{27!\times3\times2\times1} \\ \\ ^{30}C_3\text{ = 4060 different combinations} \end{gathered}[/tex]b) if you are to draw all the balls one at a time, then for the 1st it will be 30 possibilities, the next will reduce by 1 to 29 possibilities, followed by 28 possibilities, etc to the last number 1
The possible combination = 30 × 29 × 28 × 27 × 26 × 25 ......5 × 4 × 3 × 2 ×1
The above is an expansion of a number factorial. the number is 30
30! = 30 × 29 × 28 × 27 × 26 × 25 ......5 × 4 × 3 × 2 ×1
Hence, the total number of possible combinations when you draw all the balls out of the bag one at a time in factorial form is 30!
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