# Sita has 4 different and simmi has 7 different toys. Number of ways in which they can exchange their toys sothat each keeps her inital number of toys, is

Sita has 4 different toys and Simmi has 7 different toys.

The maximum number of toys they can exchange is 4 and the minimum is 1.

For the exchange of one toy:

Sita can choose in ways.

Simmi can choose in ways.

Since both of them have to exchange their toys, the total number of ways for exchanging one toy is ways.

For the exchange of two toys:

Sita can choose in ways.

Simmi can choose in ways.

Since both of them have to exchange their toys, the total number of ways for exchanging two toys is ways.

For the exchange of three toys:

Sita can choose in ways.

Simmi can choose in ways.

Since both of them have to exchange their toys, the total number of ways for exchanging three toys is ways.

For the exchange of four toys:

Sita can choose in ways.

Simmi can choose in ways.

Since both of them have to exchange their toys, the total number of ways for exchanging four toys is ways.

Therefore the total number of ways for exchanging their toys is   + + + .

Therefore the total number of ways for exchanging their toys is  28 + 126 + 140 + 35.

Therefore the total number of ways for exchanging their toys is  329.

• 0
What are you looking for?