The number of words that can be formed using the letters of the word $VOWEL$ such that the vowels always remain together is

How many $3$-digit odd numbers can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if repetition of digits is not allowed?

If $_{12}P_r = 1320$,then $r = ..........$

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?

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many $3$-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

The total number of words that can be formed using the letters $a, b, c, d, e, f$ taken $3$ at a time such that each word contains at least one vowel is: