using Permutations (nPr) solve: 1. The city plans to upgrade its Personal Identification Number (PIN) for...

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.

Solutions

Expert Solution

orchestra answered 1 year ago

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