Given Information:
- In a particular month of a year, there are 5 Tuesdays.
- All other days appear less than 5 times.

To Find:
- The first day of the next month.

Explanation:

To determine the first day of the next month, let's analyze the given information step by step.

Number of Days:
- In a month, the maximum number of days can be 31 (for months like January, March, May, July, August, October, and December).
- Since there are 5 Tuesdays in this particular month, the remaining days can be (31 - 5 = 26).

Possible Scenarios:
In order to determine the first day of the next month, we need to consider the possible scenarios for the remaining days (26) based on the weekdays they belong to.

Scenario 1: No Other Day Repeats 5 Times:
- If no other day (except Tuesday) appears 5 times, then the remaining days (26) must include 4 days from a set of 6 days (excluding Tuesday).
- In this case, the remaining days can be distributed as follows: 4 days from 6 days = (6C4) = 15 ways.
- However, since the first day of the next month can be any day of the week, there are 7 possibilities for the first day of the next month.
- Therefore, the total number of possibilities in this scenario is (15 * 7) = 105.

Scenario 2: One Other Day Repeats 5 Times:
- If one other day (except Tuesday) appears 5 times, then the remaining days (26) must include 3 days from a set of 5 days (excluding Tuesday and the repeating day).
- In this case, the remaining days can be distributed as follows: 3 days from 5 days = (5C3) = 10 ways.
- Again, since the first day of the next month can be any day of the week, there are 7 possibilities for the first day of the next month.
- Therefore, the total number of possibilities in this scenario is (10 * 7) = 70.

Scenario 3: Two Other Days Repeat 5 Times:
- If two other days (except Tuesday) appear 5 times each, then the remaining days (26) must include 2 days from a set of 4 days (excluding Tuesday and the two repeating days).
- In this case, the remaining days can be distributed as follows: 2 days from 4 days = (4C2) = 6 ways.
- As before, since the first day of the next month can be any day of the week, there are 7 possibilities for the first day of the next month.
- Therefore, the total number of possibilities in this scenario is (6 * 7) = 42.

Scenario 4: Three Other Days Repeat 5 Times:
- If three other days (except Tuesday) appear 5 times each, then the remaining days (26) must include 1 day from a set of 3 days (excluding Tuesday and the three repeating days).
- In this case, the remaining days can be distributed as follows: 1 day from 3 days = (