92. In how many ways can the letters in the word INTEGRAL be rearranged so that the third, fifth, and seventh positions are occupied by consonants?
92. The word INTEGRAL contains 5 consonant letters. Out of them, three letters can be chosen in a certain order (for the third, fifth, and seventh positions) in $A_{5}^{3}=60$ ways. The remaining 5 letters of the word can be arranged in $5!=120$ ways. In total, we get $60 \cdot 120=7200$ required arrangements of the letters in the word INTEGRAL.