Permutation and combinations!!!

[rakeshd347]

In society A, it's only acceptable to name one's children one of 10 acceptable names, either for the child's first name or for the child's middle name, though some children are not given any middle name, and it's not considered acceptable to give the child the same first and middle name. When a new child is born in society A, how many possible names can the parents consider for their child?

A 10
B 45
C 90
D 100
E 110

[vinay1983]

Ah...my nemesis.....
For me it should be 10 ways for the first name and 9 ways for the 2nd name(since same name cannot be used again)

[sanjoy18]

only first name = 10 ways
only first and middle name= 10*9= 90 ways
hence 90+10= 100

hence D

In society A, it's only acceptable to name one's children one of 10 acceptable names, either for the child's first name or for the child's middle name, though some children are not given any middle name, and it's not considered acceptable to give the child the same first and middle name. When a new child is born in society A, how many possible names can the parents consider for their child?

A 10
B 45
C 90
D 100
E 110

[ganeshrkamath]

In society A, it's only acceptable to name one's children one of 10 acceptable names, either for the child's first name or for the child's middle name, though some children are not given any middle name, and it's not considered acceptable to give the child the same first and middle name. When a new child is born in society A, how many possible names can the parents consider for their child?

A 10
B 45
C 90
D 100
E 110

Number of possibilities with first and middle name = 10C2 * 2 = 10*9/2*2 = 90
Number of possibilities with only first name = 10

Total = 100

Choose D

Cheers

[rakeshd347]

In society A, it's only acceptable to name one's children one of 10 acceptable names, either for the child's first name or for the child's middle name, though some children are not given any middle name, and it's not considered acceptable to give the child the same first and middle name. When a new child is born in society A, how many possible names can the parents consider for their child?

A 10
B 45
C 90
D 100
E 110

Thats correct the OA is D guys.

Thanks