5 A man has six coins in his pocket He agrees to give one co

5. A man has six coins in his pocket. He agrees to give one coin to his son and one coin to his daughter. How many ways can this be done? 6. In how many different ways can one call on the numbers 1, 2, 3, 4, 5? 7. In dialing a telephone number, one has to select seven slots, the first two for the letters of the exchange, and then five digits to identify the telephone in that exchange. The telephone dial contains ten slots, one for each of the digits 0, 1, 2, ..., 9, but letters appear in only eight of these slots. If the fist number cannot be a zero, how many different telephone numbers, distinguishable as dialed, are possible? 8. Flow many three-digit even integers can be formed from the digits 1, 5, 6, and 8, with not digit repeated?

Solution

5.
It can be done 6 C 2 ways = 6*5/2*1 = 15

6.
One call the numbers in 5! ways = 120

8.
A number could be even only it ends with either
0,2,4,6,8
Here we only have 2 nmbers that match with the third digit.

Among the three digit word selected, the third letter be 6 or 8

i.e selection of 3rd digit is 2 ways
selection of second digit, 1st digit 3*3
Possible ways are = 3*3*2 = 18