How many words of $7$ letters can be formed by selecting $4$ consonants and $3$ vowels from $6$ consonants and $5$ vowels?

How many numbers greater than $10$ lakh can be formed using the digits $2, 3, 0, 3, 4, 2, 3$?

How many $4$-digit even numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6$ without repetition?

The number lock of a suitcase has $4$ wheels,each labelled with ten digits,i.e.,from $0$ to $9$. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

How many words can be formed using the letters of the word $ARRANGE$ such that the consonants appear in alphabetical order?

Five students are to be arranged on a platform such that the boy $B_1$ occupies the second position and the girl $G_1$ is always adjacent to the girl $G_2$. Then,the number of such possible arrangements is