Probability既難題 10分

a)
9 * 9 * 8 * 7 = 4536

first digit not zero,
second digit has 9 choices, may contain zero

b)
9 * 10 * 10 * 10 / 2 = 4500

all numbers formed with repetition / 2,
half even and half odd

c)
10 * 9 * 4 - 9 - 9 * 3 = 324

3 digits same and the other not equal (but first digit may contain zero) = 10 * 9 * 4

numbers with first digit zero
0111, 0222 ...0999 ( 9 個 )
and 0100, 0010, 0001, 0200, 0020, 0002 ..... ( 9 * 3 個 )

4 decimal digits include the figures from .0000 to .9999; there are totally 10,000 figures.

a. possibility of no same digit twice (from .0000 to .9999)
= 10/10 * 9*10 * 8 /10 * 7/10
= 5,040 / 10,000

the number of strings of 4 decimal digits not contain the same digit twice
= 5,039

b. there are 1/2 probability with an even digit from .0000 to .9999, that i.e 5,000 strings of decimal digits with an even digit.

c. possibility of no same digit twice (from .0000 to .9999)
= 10/10 * 1*10 * 1 /10 * 9/10 * 4 (“*4* means there are 4 cases with 3 common digit)
= 360 / 10,000
The number of strings of decimal digits with 3 common digit
= 360