Question

8. Four married couples have bought 8 seats in the same row for a concert. Ia how manry different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives? 9. A machinist produces 22 items during a shift. Three of the 22 items are defective and the rest are not defective. In how many different orders can the 22 items be arranged if all the defective items are considered identical and all the non-defective items are identical of a different class?

8&9

Answer 1

In question 8

With no restriction

Any member can sit any place so at first place any of eight can sit thn at after his/her sitting

At second place anyone of seven remaining can sit and so on...

So ways are 8! = 40320

B)

When couples sit together

Any of the 2 in a couple sit first then another person

Similarly all 4 couples sit

And this can be done in 4 different ways...

So 64 ways

C) whn all husband sit together to right of all wifes

Any of the female sit at first place thn any of remaining 3 women at second place...so on

Similarly with men

So ways are

576.

Question 9

Any defective or non defective item

19!*3!

Ways

Thanks