help with math grade 9 integer math games

Question: Answer: ..

Question: How many words of different 4 letters can be formed out of 7 capital letters, 3 vowels and 8 consonants, if each word starts with a capital letter and contains at least one vowel? Answer: Any capital letter can be chosen as the first letter of each word. So there are 7 ways of..

Let n be a positive integer. The continued product of first n natural numbers is called factorial n and is denoted as ..

Let n be a positive integer. The continued product of first n natural numbers is called factorial n and is denoted as n..

How many numbers are there between 100 and 1000 such that every digit is either 2 or 9..

i) 1 + 4 + 7 + 10 + ... is a series in which first term is 1, second term is 4, third term is 7 and so on. ii) 3 - 9 + 27 - 81 + ... is also a series in which the first term is 3, second term is -9, third term is 27 and so ..

Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we get ..

The number of permutations of n dissimilar things taken r ..

Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..