[數學] F.5 概率應用題Level 1 (Eng.)

(Question 1)
Method 1 :
3 _ _ _
• Put 1 of the rest 5 digits (1, 2, 6, 7, 9) as the hundreds digit (5).
• Put 1 of the rest 4 digits as the tens digit (4).
• Put 1 of the rest 3 digits as the units digit (3)

Number of 4-digit numbers formed
= 5 x 4 x 3
= 60

Method 2 :
Number of 4-digit numbers formed
= 5P3
= 5!/2!
= 60


(Question 2)
Method 1 :
X X _ _ _ _
• Put 1 of the 5 letters (A to E) as the first letter (5).
• Put 1 of the 4 letters as the second letter (4).
• Put 1 of the 10 digits (0 to 9) as the first digit (10).
• Put 1 of the rest 9 digits as the second digit (9).
• Put 1 of the rest 8 digits as the third digit (8).
• Put 1 of the rest 7 digits as the fourth digit (7).

Number of possible staff numbers
= 5 x 4 x 10 x 9 x 8 x 7
= 100800

Method 2 :
Number of possible staff numbers
= 5P2 x 10P4
= (5!/3!) x (10!/6!)
= 100800