Find the number of arrangements from letters of word ENGINEERING such that
i) 3 N’S come together
ii) 3 N’S come together but 3 E’S do not come together

i) Given word ENGINEERING contains 11 letters of which there are 3N’s, 3E’s, 2G’s, 2I’s, 1R The no. of arrangements in which all the 3 N’s
are come together$=\frac{9!}{3!2!2!}$

ii) The no. of arrangements in which 3 N’s come together and 3 E’s come together$=\frac{7!}{2!2!}$

The no. of arrangements in which 3 N’s come together and 3 E’s do not come together$=\frac{9!}{3!2!2!}-\frac{7!}{2!2!}=15120-1260=13860$