First we calculate for the total number of possibilities (permutation) to select 4 disks from the container:
Total number of possibilities = 10 * 9 * 8 * 7
Total number of possibilities = 5040
Now let us find the 4 disks that will result in a range of 7.
Range = highest number – lowest number
The pair of highest and lowest number that will result in range of 7 is: (1 & 8), (2 & 9), (3 & 10)
As a basis of calculation, let us use the pair 1 & 8.
There are four possible ways to select 1 and three for 8.
Arrangements of maximum and minimum pair = 4 * 3
Arrangements of maximum and minimum pair=12
Now we need to calculate for the remaining 2 disk. There are 6 numbers between 1 & 8. The total possibilities for selecting 2 disk from the remaining 6 is:
Possibilities of selecting 2 disk from remaining 6 = 6 * 5
Possibilities of selecting 2 disk from remaining 6 = 30
Therefore, the total possibility to get a range of 7 from a pair of 1 & 8 is:
Total possibility for a pair = 12 * 30
Total possibility for a pair = 360
Since there are a total of three pairs (1 & 8), (2 & 9), (3 & 10):
Total possibilities of the 3 pairs = 360 * 3
Total possibilities of the 3 pairs = 1080
Therefore:
Probability = Total possibilities of the 3 pairs / Total number of possibilities
Probability = 1080 / 5040 = 3 / 14 (FINAL ANSWER)
