Selection of one particular member can be done in 1C1 = 1 way.

After the selection of the particular member, we are left with 9 members and for the delegation, we need 4 members more. So selection can be done in 9C4ways.

Reqd no. ofways of selection= 1C1/ 9C4 = 1X 9 X 8 X 7 X 6/24 = 126

(ii) When one particular person has to be always excluded from the

5-member delegation, we are left with 10 - 1 = 9 persons. So selection can be done in 9C

ways.

:.Reqd no.= 9C5 = 126

2.

In a party every person shakes hand with every other person. If there was a total of 210 handshakes in the party, find the no. of persons who were present in the party.

No. of identical balls= 4 and no. of identical boxes= 6

Now, distributing 4 identical balls among 6 identical boxes when not more than one ball goes into a box, implies to select 4 boxes from among the 6 boxes, whicl: can be done in 6C4 = 6!/4!x2! = 15 ways

8.

How many words can be formed out of the letters of the word BANANA so that the consonants occupy the even places?

The word BANANA contains 6 letters out of which A occurs thrice and N occurs twice.

The 3 consonants 8 and N (which occurs twice) can be arranged 3 at the 3 even places 2, 4 and 6 in 3!/2! = 3 ways

The remaining 3 odd places can be arranged with triple A in 3!/3! = 1 way

so, required number = 3 x 1 = 3 ways

9.

A man wants to go abroad by ship and return by air. He has a choice of 4 ships to go and 5 airlines to return. In how many ways can man perform his journey?