outcomes and numbers

Question

nvolving the selection of digits from a set. Assume that you select digits from the set {1,2,4,7} to form a number between 10 and 700.

(1) How many such numbers can be formed if digits are not repeated?

 

(2) How many such numbers can be formed if digits can be repeated?

Answer 1

(1) If digits are not repeated:

# of two digit numbers = 4*3 =12 (4 options for tens digit as all the 2-digit numbers starting with 1,2,4 or 7 will be more than 10 and then remaining with 3 options for ones place)

 

# of three digit numbers =3*3*2=18(As we can not use 7 at hundreds place so for hundreds place we have only 3 choices ,for tenth place we will have 3 choices as now we can use 7 also and for ones place only two choices)

 

total = 12+18=30

 

(2) If digits can be repeated:

 

# of two digit numbers = 4*4 = 16 (as all the 2-digit numbers starting with 1,2,4 or 7 will be more than 10 )

 

# of three digit numbers = 3*4*4 =48 (as we can't use digit 7 at first place because number should be less than 700,so only 3 choices for hundreds place and 4 choices for tens and ones place)

total = 16+48 =64