How many arrangements of four 0's (zeroes), two 1's and two 2's are there in which the first 1 occur before the first 2?

How many different five-letter words can be formed using the letter from the world APPLE?

I have an amount of Rs. 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?

A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?

How many 5-digit positive integers exist the sum of whose digits are odd?

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