Answer:
Step-by-step explanation:
There are 5numbers and 3 letters. Each number can be one among the 10 possible.
Each letter is 1 among the 26 available.
a)The number of possible unique serial numbers are
10^5x 26³
The number of 5 number combinations each different (order important) is 5!(10/5)= 30240
The number of 3 letter combinations each different (order important) is 3!(26/3)=15600
The required probability (that all symbols are different if one laptop is picked at random with equal probability) is
15600x3240/ 10^5x 26³=0.2684
b) The first letter must be at least 4 to be largest among the 5 numbers. So the first letter can be one of . 4,5,6,7,8,9..
The number of 5 number combinations each different and starting with 4 (order important) is .
4!=24
The number of 5 number combinations each different and starting with 5 (order important) is .
4!(5/4)= 120
The number of 5 number combinations each different and starting with 6 (order important) is .
4!(6/4)= 360
The number of 5 number combinations each different and starting with 7 (order important) is .
4!(7/4)= 840
The number of 5 number combinations each different and starting with 8 (order important) is
4!(8/4)= 1680
The number of 5 number combinations each different and starting with 9 (order important) is .
4!(9/4)= 3024
Thus, there are
The required probability ( that all symbols are different and the first number is the largest among the numbers) is
15600* 6040/10^5x 26³= 0.0537
