Question

A bank assigns random 4-digit numbers for atm access codes. in each code, no digit is repeated. use combinations to find the number of ways that 4 digits can be chosen from 10 digits, if order is not important. what is the probability that edmund is assigned a code with the digits 6, 7, 8, and 9 in any order

Answer 1

The number of ways to select 4 digits from 10  digits is
₁₀C₄ = 10!/(4!*6!) 
       = (10*9*8*7*6!)/(4*3*2*1*6!)
       = (10*9*8*7)/(4*3*2)
       = 210 

If order is not important, the number of arrangements of 6,7,8,9 in any order is
4! = 4*3*2*1
    = 24
The probability that these 4 digits are assigned is
24/210 = 0.1143