Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

A Five digits number is written down at random. Find the probability that number is divisible by 5 and no two consecutive digits are identical.
Asked by rairp2017 | 27 May, 2021, 12:21: AM
Expert Answer
Let us find out  first , how many ways a 5 digit number is written
 
 
Let us consider position number of left most digit is 1, right most digit is 5 and position number of
in-between digita are assigned as shown in above figure.
 
Number of ways of writing digits at position number 1 is 9 because digit zero can not be chosen out of 10 digits .
 
Number of ways of writing digits at position number 2 is 9 because one digit is already selected for position number 1.
 
Number of ways of writing digits at position number 3 is 8 because two digits are already selected for previous positions.
 
Number of ways of writing digits at position number 4 is 7 because three digits are already selected for previous positions. 
 
Number of ways of writing digits at position number 5 is 6 because four digits are already selected for previous positions.
 
Hence number of ways writing the 5 digit number , N = ( 9 × 9 × 8 × 7 × 6 )
 
-----------------------------------
 
Let us find out  now , how many ways a 5 digit number that is divisible by 5 is written
 
To get a 5-digit number that is divisible by 5 , digit in units place hase to be either 5 or 0 . 
 
Number of ways of writing digits at position number 1 is 9 because digit zero can not be chosen out of 10 digits .
 
Number of ways of writing digits at position number 2 is 8 because one digit is already selected for position number 1
and either 0 or 5 is reserved for position number 5.
 
Number of ways of writing digits at position number 3 is 7 because two digits are already selected for previous positions
and either 0 or 5 is reserved for position number 5.
 
Number of ways of writing digits at position number 4 is 6 because thre digits are already selected for previous positions
and either 0 or 5 is reserved for position number 5.
 
Number of ways of writing digits at position number 5 is 2 only   
 
Hence number of ways writing the 5 digit number that is divisble by 5, n = ( 9 × 8 × 7 × 6 × 2 )
 
Probability of writing a 5 digit number that is divisible by 5 , P = n/N
 
P = ( 9 × 8 × 7 × 6 × 2 ) / ( 9 × 9 × 8 × 7 × 6 )  = 2 / 9 
Answered by Thiyagarajan K | 20 Sep, 2021, 11:53: PM
CBSE 12-science - Maths
Asked by lovemaan5500 | 03 Oct, 2019, 05:47: AM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT
Season Break Offer!
Get 60% Flat off instantly.
Avail Now
×