a person must set a password consisting of 5 digits, how many passwords are poss

Question

a person must set a password consisting of 5 digits, how many passwords are possible if 1. The first number must be a 7 and no repetition is allowed. 2. The first number is a 7, the last number cannot be a 0, and no repetition is allowed. a person must set a password consisting of 5 digits, how many passwords are possible if 1. The first number must be a 7 and no repetition is allowed. 2. The first number is a 7, the last number cannot be a 0, and no repetition is allowed. a person must set a password consisting of 5 digits, how many passwords are possible if 1. The first number must be a 7 and no repetition is allowed. 2. The first number is a 7, the last number cannot be a 0, and no repetition is allowed.

Explanation / Answer

Numerator of ways in which a five digit password can be set without replacement is 10P5 = 30240

1.) The first number can be 7 in one way. The remaining 4 digits can be chosen from 9 digits in 9P4 = 3024 ways

Therefore total number of passwords possible is 3024 × 1 = 3024

2.) The first number 7 can be possible in only 1 way

If zero is included in any of the next three places

Then number of possible ways to choose the remaining 3 places is 8P3 = 336

If zero is not included in the next 3 place than the number of ways to choose the digits for these three plces will be 8P3 = 336

Since the last digit cannot be zero and 4 digits have already been used in the first 4 place the last digit can be chosen from the remaint5 digits in 5 ways

Therefore total number of passwords

= (1 × 336) + (1 × 336 × 5) = 2016

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.