The completion of tasks relies on having enough data and reliable tools for efficiently solving problems. In a diversified mathematics field, choosing the right method is key in using the right formulas and methods. As a tool in completing the task, the use of combination method is essential in determining the probability solutions. As explained by Barboianu (2013), the rule of combinations focuses on the determination of ways for the selection of defined items Q times, from an array of N objects, without the possibility of repetition. Hence, by applying combination formula, it gets possible in solving the problem.
As shown from Barboianu (2013), the combination formula is nCr= n! / (n-r)! r!
1st Step: Finding for 3 boys from the sum of sum of 15 boys will be:
= 15! / ((15-3)! 3!) = 455 varied number of ways in which the 3 boys have a chance of being chosen from the sum of 15 boys
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2nd Step: Selecting 7 girls from 30 girls, i.e., 30C7
This will be 30! / ((30-7)! 7!) = 2,035,800 which indicates the varied number of ways that the 7 girls could finally get selected from the total of 30 girls
3rd Step: The selection of 10 students from the sum of 45, i.e., 45C10
= 45! / ((45-10)! 10!) = 3,190,187,800 which shows various ways in which 10 students can possibly get selected from sum of the overall 45 students
Step 4: The determination of the asked probability is:
Pr. = (455*2035, 800)/3,190,187,800 = 0.29036, (by using excel software)
By writing the answer in two (2) decimal places there is getting of 0.29, which shows the probability that there is the selection of 3 boys out of desired selection of 10 students, from the total number of 45 students of girls and boys.
Reference
Barboianu, C. (2013). Mathematics of slots: Configurations, combinations, probabilities . Infarom Publishers.
