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:

Friend l am not able to solve (a) but I can help you with (b):

Here it is:

Using fundamental principle of counting:

No of three digit nos. having three different digits= 5×4×3=60(Ans)

Step-by-step explanation:

Answer 2

Answer:

445 and 380

Step-by-step explanation:

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

a) number of 3 digit combinations:

• 111 to 555

• 555-111+1= 445

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b) to be excluded:

1. same 3 digits

• 111, 222, 333, 444, 555 = 5

2. same 2 digits

• 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

Total number of combinations to be excluded: 5+3*4*5= 65

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

Answer: total combinations are 445, and 3 different digit combinations are 380