Q: How many ways can 5 teddy bears, 6 toy trucks, 5 dolls and 1 toy car be distributed among 17 children if each child is to receive 1 item?
A: 17!/(5!*6!*5!*1!) = 34,306,272
Is this correct?
That doesn't look right to me. I think you did it wrong, but I don't know how.
If all the teddy bears and trucks etc are identical then it will be
17! / (5!6!5!1!)
Now that you have edited your question it is correct.
If you edit your post please have the courtesy to state what you have changed.