Ace Test series: Combinatory - Permutation and Combinations

Question

My approach :- ways to arrange 6 distinct symbols = 6!

Place 2 blanks between each symbol, remaining blanks = 2

Now these 2 blanks can be placed in any of 5 places so = 5*5= 25 ways

Total ways = 6!*25 = 18000

But the answer given in 10800 :(

please someone tell me where I am wrong.

Comments

for putting two remaining blanks,

case 1: when both blanks are put b/w same pair- $5$

case 2: when both blanks are put b/w different pairs- $\binom{5}{2} = 10$

total ways of adjusting blanks and symbols, $6!*(\binom{5}{2}+5)=10800$

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Got it

Thank you sir :)

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Thank You