using Permutations (nPr) solve:
1. The city plans to upgrade its Personal Identification
Number (PIN) for each of its employees. The PIN will consist of 7
characters defined, in three independent categories, as
follows:
• The first two characters are uppercase letters, no letter to
be repeated.
• The next three characters are digits, no digit to be
repeated.
• the last two characters are letters (uppercase or
lowercase), but no letter is to be repeated. For example, aA is
acceptable as they are different characters.
Find the total number of possible PIN.
2.Using only the digits from {0, 1, 2, 3, 4, 5}, find the
total number of numbers greater than 500 if each digit can only be
used once.
using Combination (nCr) solve:
1. On a shopping spree at DownTown Plaza, you wish to acquire
electronics, shoes, and jewelry. After browsing, there are 5
electronic devices suitable to your needs, 10 pairs of shoes
satisfying your taste, and 12 jewelry pieces that woud certainly
enhance your attributes. Unfortunately, you can only leave with 2
from each category. Find the total number of possible
choices.
2. Following from the previous problem, after careful
consideration, you decide to get the iPhone XR. This, however,
won’t allow you to get another electronic device. Moreover, you can
only afford one more category. Find the total number of choices
possible.