How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$,if each number starts with $67$ and no digit appears more than once?

The number of words (with or without meaning) that can be formed from all the letters of the word $LETTER$ in which vowels never come together is

The numbers $1, 2, 3,$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. $A$ person draws two slips from the box,one after the other,without replacement. Describe the sample space for the experiment.

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits such that the odd digits occupy even places?

The number of odd numbers greater than $6,00,000$ that can be formed by using the digits $3, 6, 7, 8, 9, 0$ without repetition is

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.