The number of permutations of alphabets of the word “ENSHRINE” in which no two alike alphabets are together is equal to

Step-by-step solution

E E N N S H R I Let the event E :   E ' s are together and event N :   N ' s are together Required permutations = Total permutations - n E ∪ N = 8 ! 2 ! 2 ! - 7 ! 2 ! + 7 ! 2 ! - 6 ! = 10080 - 2520 - 2520 + 720 = 5760