5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is

All possible words (with or without meaning) the contain the word 'GENTLE' are formed using all the letters of the word 'INTELLIGENCE'. Then, the number of words in which the word 'GENTLE' appears among the first nine positions only is

$$ { }^{20} P_5-{ }^{19} P_5= $$

If all the letters of the word ACADEMICIAN are permuted in all possible ways, then the number of permutations in which no two $A^{\prime} s$ are together and all the consonants are together is