Question

If you have the following set of numbers: {1,5,6,0,8,9} and you want to form three-digit numbers. The numbers can not be repeated.
to.

a. How many numbers can be formed?
b. How many even numbers can be formed?
c. How many numbers greater than or equal to 560 can be formed?

Answer 1

a)

for first digit we have 5 choices (Ex cept 0) for second remaing 5( including ) and for 3rd digit 4 chices are there

therefore total 3 digt numbers that can be formed =5*5*4=100

b) for odd numbers -for last digit we have 3 choices (from 1,5,9) ; for first digit remaining 5 choices and for middle digit 4 choices ; therefore total odd numbers =3*5*4=60

hence total 3 digit event numbers =total numbers -total odd numbers =100-60 =40

c)

number which starts with 5: have 3 choices for 2 nd digit (6,8,9) and remaining 4 choices for 3rd digit

=3*4=12

number which starts with more than 5: for first digit 3 choices (6,8,9) for 2nd remaing 5 and for 3rd remianing 4 =3*5*4=60

hence total number which are greater than 560 =12+60 =72