Question

How many ways can the letters STREETS be placed in recognizably different orders?

1. How many of the orderings of part (a) begin with T?
2. In how many of the orderings of part (a)are the two E’s adjacent?

Answer 1

STREETA CAN BE placed recognizably different order in 630 different ways. As 7 letters. Arrange in order with 7 factorial since here identical two S's, two T's and two E's

so divide 7 factorial by (2 factirial *2 factorial *2 factorial,) =630

2) when order begins with T then One T is fix at 1st poation than there remains 6 letters aarnge them where only 2 identical letters two S's and two E's here we get 180 orders possible=6 factorial divide by (2 factorial *2 factorial)

3) when Two Es are adjacent than by taking two EE AS a single letters than there only 6 letters to orders with identical values two T's and two S's here we get 180 orders possible =6 factorial divide by (2 factorial *2 factorial)

Solution file is attached go through it

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