Answer:
a) 5,000 b) 3,600
Step-by-step explanation:
a) there are four different slots, and for the first three slots there are a possibility for 10 different numbers and in the last slot there can only be 5 different numbers. So you get 10 x 10 x 10 x 5 which leaves you with 5,000 possibilities
b) the same thing as above but know you have fewer numbers 10 x 9 x 8 x5 which gives you 3,600 possibilities
The total number of choices for part (a) is 5000, and the total number of choices for part (b) is 2520.
A permutation can be defined as the number of ways a set can be arranged, order matters but in combination, the order does not matter.
We have 10 digits(0 to 9)
(a) In the first place, second place, and third place we can put 0-9 means a total of 10 numbers.
In fourth place, we can only put 1, 3, 5, 7, and 9 means a total of 5 digits.
So total number of choices = 10×10×10×5 = 5000
(b) When repetition is not allowed
When we put 1 at last place, then a number of choices:
=9×8×7×1 = 505
Similarly for 3, 5, 7, and 9 the number of choices same as placing 1 at last place, then a number of choices:
= 505+505 +505+505+505
= 2520.
Thus, the total number of choices for part (a) is 5000, and the total number of choices for part (b) is 2520.
Learn more about combination here:
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