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?

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ?

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 letters are used at a time,

Find $n$ if ${}^{n–1}P_3 : {}^nP_4 = 1 : 9$.

In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S,

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Find $r$ if (i) ${}^5P_r = 2 \cdot {}^6P_{r-1}$

How many 4-digit numbers are there with no digit repeated?

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (iii) all letters are used but first letter is a vowel?

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions ?

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet ?

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed?

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?

If ${}^nC_8 = {}^nC_2$, find ${}^nC_2$.

Determine $n$ if (i) ${}^{2n}C_3 : {}^nC_3 = 12 : 1$

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?