A committee of $8$ is to be formed from $6$ girls and $8$ boys. In how many ways can it be done when the committee consists of at least $4$ girls?

In how many ways can $4$ cards be selected from a pack of cards such that at least one of the four cards is of the red suit?

Sunita and her sister Varsha are playing a game. They have eight identical white balls and eight identical blue balls, respectively. In how many ways can they arrange the balls in a row so that no two blue balls are together?

Mr. Kashyap, a great statistician, wants to set a code in a computer folder using different digits from $1, 2, 3, 4, 5,$ and $6$. If at least two digits are required to form a code, in how many ways can the code be formed?

 In how many ways can one card be drawn from a full pack of $52$ cards such that it is black?

Sunita is playing with some numbers. How many numbers greater than a million can be formed using the digits $4, 5, 0, 3, 4, 5$ and $4$?

How many words can be made with the letters of the word BEAUTIFUL if the vowels and consonants are in alternate positions?