Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
Share
Notifications

View all notifications
Advertisement

A Five-digit Number is Written Down at Random. the Probability that the Number is Divisible by 5, and No Two Consecutive Digits Are Identical, is - Mathematics

Login
Create free account


      Forgot password?

Question

A five-digit number is written down at random. The probability that the number is divisible by 5, and no two consecutive digits are identical, is

Options
  • \[\frac{1}{5}\]

     
  • \[\frac{1}{5} \left( \frac{9}{10} \right)^3\]

     
  • \[\left( \frac{3}{5} \right)^4\]

     
  • None of these

     

Solution

Let number be abcde
Case 1 : e = 0
abc can be filled in 9 × 9 × 9 ways
c = 0 ⇒ 9 × 8 × 1 ways and d has 9 choices
c ≠ 0 ⇒ (9 × 9 × 9 – 9 × 8 × 1) = 657
in the case d has 8 choices ⇒ 657 × 8
Total case = 9 × 8 × 1 × 9 + 657 × 8 ⇒ 5904
Case 2 : e = 5
If c = 5,
if a ≠ 5 then abc can be filled in 8 × 8 × 1 = 64 ways
if a = 5 then abc can be filled in 1 × 9 × 1 = 9 ways
if c ≠ 5, then first 3 digits can be filled in 729 – 64 – 9 = 656 ways
here d has 8 choices
No. of member ending in 5 and no two consecutive digits being identical ​⇒ (64 + 9) × 9 + 656 × 8

⇒ 5905
​Total cases ⇒ 5904 + 5905 ⇒ 11809
\[\text{ Required Probability } = \frac{11809}{90000}\]

Hence, None of these

 
  Is there an error in this question or solution?
Advertisement

APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
MCQ | Q: 18 | Page no. 29
Advertisement

Video TutorialsVIEW ALL [1]

A Five-digit Number is Written Down at Random. the Probability that the Number is Divisible by 5, and No Two Consecutive Digits Are Identical, is Concept: Bernoulli Trials and Binomial Distribution.
Advertisement
View in app×