The total number of 4 digit numbers in which the digits are in descending order is:
Approved Tutor Answer9 Months agoTo find the total number of 4-digit numbers where the digits are in descending order, we need to consider the digits available. The digits can range from 0 to 9, but since we want a 4-digit number, the first digit cannot be 0.
When the digits are in descending order, each digit must be unique. Therefore, we can only select from the digits 1 to 9 for the first digit and include 0 for the remaining digits. This means we can choose any 4 digits from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
We need to choose 4 digits from the 10 available digits. The number of ways to choose 4 digits from 10 is given by the combination formula:
In this case, n = 10 and r = 4:
C(10, 4) = 10! / (4!(10 - 4)!) = 10! / (4! * 6!) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1) = 210
Thus, the total number of 4-digit numbers with digits in descending order is 210. Therefore, the correct option is (a) 210.
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