Question

there are three dials on a combination lock
each dial can be set too 1,2,3,4,5
514 is one way the dial can be set

a)work out the number of different 3 digit numbers that can be set

b)how many of the possible 3 digit numbers have 3 different digits

Answer 1

Answer:

Total combinations are 445, and 3 different digit combinations are 380.

Step-by-step explanation:

Each dial can be set to $1, 2, 3, 4, 5$

a) the number of 3-digit combinations:

$111$ to $555$

$555 - 111 + 1 = 445$

b) The possible 3-digit numbers have 3 different digits to be excluded:

1. same 3 digits

$111, 222, 333, 444, 555 = 5$

2. Same 2 digits

Simplifying the values as:

• $112/113/114/115 = 4$
• $221/223/224/225 = 4$
• $331/332/334/335 = 4$
• $441/442/443/445 = 4$
• $551/552/553/554 = 4$
• $121/131/141/151 = 4$
• $212/232/242/252 = 4$
• $313/323/343/353 = 4$
• $414/424/434/454 = 4$
• $515/525/535/545 = 4$
• $122/133/144/155 = 4$
• $211/233/244/255 = 4$
• $311/322/344/355 = 4$
• $411/422/433/455 = 4$
• $511/522/533/544 = 4$

The total number of combinations to be excluded: $5+3*4*5= 65$

Possible 3-digit numbers with 3 different digits $= 445- 65= 380$

The sum of combinations is 445, and 3 different digit combinations are 380.

#SPJ3

Answer 2

Answer:

Step-by-step explanation:

A) 5 x 5 x 5 = 125 different combinations since each letter slot has 5 different numbers to choose from

B) 5 x 4 x 3 = 60 with different digits since the options would decrease by one in order for them to have different digits

Is definitely correct as checked by mathswatch and exam question mark scheme