Photo AI

Out of 10 contestants, six are to be selected for the final round of a competition - HSC - SSCE Mathematics Extension 1 - Question 8 - 2020 - Paper 1

Question 8

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 th... 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 8 - 2020 - Paper 1

Step 1

Calculate the number of ways to select 6 contestants

96%

114 rated

Answer

To determine the number of ways to select 6 contestants from 10, we use the combination formula:

$C(n, r) = \frac{n!}{r!(n-r)!}$

Here, we have ( n = 10 ) and ( r = 6 ):

$C(10, 6) = \frac{10!}{6! \, 4!}$

Step 2

Calculate the arrangement of the top 4 contestants

99%

104 rated

Answer

Next, we need to arrange the selected 4 contestants in 1st, 2nd, 3rd, and 4th places. The number of permutations for 4 contestants is given by:

$P(4) = 4!$

Step 3

Combine the results

96%

101 rated

Answer

To find the total number of ways to carry out this process, we multiply the number of ways to select the contestants by the number of arrangements:

$\text{Total Ways} = C(10, 6) \times P(4) = \frac{10!}{6! \, 4!} \times 4! = \frac{10!}{6!}$

Join the SSCE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;