How many lists of length 5 with no repetition can be made fr

How many lists of length 5, with no repetition, can be made from number 123456789 that begins with an even number or ends with an even number or both?

Solution

SEE CASE 1

WHEN NO: BEGINS WITH EVEN.

SO AT FIRST PLACE, WE HAVE ONLY 4 CHOICES THAT ARE 2,4,6,8, AND AFTER EACH STEP WE WILL HAVE ONE LESS NUMBER AVAILBALE FROM THE OPTION BECAUSE THE NUMBERS CANNOT REPEAT.

SO AT FIRST WE HAVE 4 CHOICES

AT SECOND WE HAVE 8 CHOICE( AS FROM ABOVE 1 NUMBER IS CONSUMED)

AT THIRD 7 CHOICES

AT 4TH 6 CHOICES

AT 5TH 5 CHOICES

SO TOTAL NUNBERS CAN BE FORMED ARE 4*8*7*6*5 =6720

CASE 2 WHEN NUMBER ENDS WITH EVEN-

SAME AS ABOVE BT THE 4 CHOICE WE WILL HAVE IN LAST DIGIT OPTION

SO TOTAL WAYS = 6720

CASE 3

WHEN ENDS WITH EVEN AND BEGINS WITH EVEN

NOT AT FIRST DIGIT WE HAVE 4 CHOICE THERE FORE AT END WE HAVE 3 CHOICES.

AND IN 3RD 4TH AND 5TH WE WILL HAVE 7,6,5 CHOICES

TOTAL NUMBER WILL BE = 4*3*7*6*5=2520

HENCE TOTAL NUMBERS CAN BE FORMED ARE 6720+6720+2520=15960