Problem Solving

Gordon buys 5 dolls for his 5 nieces. The gifts include two identical S beach dolls, one E, one G, one T doll. If the youngest niece doesn't want the G doll, in how many different ways can he give the gifts?

is my application of slot method correct ?

lets treat 2 identical dolls as different
since youngest girl has restrictions, fulfill her choice first.
youngest girl can get the dolls in 4 ways
then all other girls can be given dolls in 4*3*2*1 ways = 24 ways
total no. of ways = 4*24=96

Now, since there are 2 identical dolls, we need to divide(reduce) above arrangements by no. of ways identical dolls affected(increased) above arrangements i.e. 2!=2

Hence, total arrangements = 96/2=48