Question

solve the question from permutation and combination. Zoom to view.​

Answer 1

Step-by-step explanation:

There are 1 G , 3 A , 1 N , 1P , 1T and 1I

Now each case

I is at the 4th place

All A occupies first three places

4! = 24

I is at the 5th place

All A occupies first three of 4 places

$\binom{4}{1} \times3!\times \frac{4!}{3 !}=96$

I is at the 6th place

$\binom{4}{2} \times2!\times \frac{5!}{3 !} = 120$

Similarly other cases

$\binom{4}{3} \times1!\times \frac{6!}{3 !} = 80$

$\binom{4}{4} \times3!\times \frac{7!}{3 !}= 210$

Total =530ways