Question

Find the probability of forming 4 digits number using 1,2,3,4,5,6,7,8 without any repetition? 50 60 70 80

Answer 1

the probability of forming 4 digits number using 1,2,3,4,,5,6,7,8,9is 70

Answer 2

Answer: $\dfrac{105}{256}$

Step-by-step explanation:

Given digits : 1,2,3,4,5,6,7,8

Total number of ways to make a 4 digits number from the given 8 digits is given by :-

$8^4=4096$

Also, if repetition is not allowed , then we use permutation to find the number of ways to arrange things.

Permutation of n things where r things taken at a time is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Number of ways to make 4 digits number using 1,2,3,4,5,6,7,8 :

$^8P_4=\dfrac{8 !}{(8-4)!}=\dfrac{8\times7\times6\times5\times4!}{4!}\\\\=1680$

Now, the probability of forming 4 digits number using 1,2,3,4,5,6,7,8 without any repetition will be :_

$\dfrac{1680}{4096}=\dfrac{105}{256}$

Hence, Required probability : $\dfrac{105}{256}$