1:There are 7 seats in the family new van. if 4 of the 7 family members can drive,how many possible seating arrengements are there for a family trip in the van?

Question

2:How many even five digit numbers can be formed using only the numbers through 1 and 7?

Answer 1

first the driver in the driver seat
4 possible
that leaves three with the other three to choose the other six seats. How many arrangements of those six people?
the first one has 6 choices, the second 5 choices .....
6*5*4 etc or 6!
so 4 * 6!

even ends in 2 , 4 , 6
so the fifth digit must be 2, 4, or 6
the fourth must be 1, 2 , 3 , 4 , 5 ,6 , 7 seven choices
the third - 7 choices
the second -- 7 choices
he first - 7 choices
so
2 * 7^4

Answer 2

3*7^4