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

Question

Mathematics

Brenna Church

7 April, 02:21

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

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Cyrus Swanson · 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