Out of 10 contestants, six are to be selected for the final round of a competition - HSC - SSCE Mathematics Extension 1 - Question 10 - 2020 - Paper 1
Question 10
Out of 10 contestants, six are to be selected for the final round of a competition. Four of those six will be placed 1st, 2nd, 3rd and 4th.
In how many ways can thi... show full transcript
Worked Solution & Example Answer:Out of 10 contestants, six are to be selected for the final round of a competition - HSC - SSCE Mathematics Extension 1 - Question 10 - 2020 - Paper 1
Step 1
Selecting 6 Contestants from 10
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Answer
To select 6 contestants from a total of 10, we can use the combination formula:
C(n,r)=r!(n−r)!n!
In our case, we have:
C(10,6)=6!⋅4!10!
Calculating this gives us several ways to choose 6 contestants.
Step 2
Arranging 4 Contestants in Order
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Answer
Next, we need to arrange 4 of the chosen 6 contestants. The number of ways to arrange r items is given by:
P(r)=r!
For our case:
P(4)=4!
Thus we find the number of arrangements for 4 selected contestants.
Step 3
Total Ways to Conduct the Process
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Answer
Finally, we calculate the total number of ways to conduct the entire selection and arrangement process as follows:
Total Ways=C(10,6)×P(4)=6!⋅4!10!⋅4!=10!/6!
Therefore, the total number of ways this process can be carried out is represented by option A: 6!10!.
