How many numbers are there between $100$ and $1000$ including $100$ such that every digit is either $2$ or $5$.
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1Have you tried anything? Can you answer the same question if we want integers between $10$ and $100$? – lulu Oct 29 '15 at 13:04
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Do you mean divisible by 2 or 5? – Soham Oct 29 '15 at 13:04
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No it means every digit in that number is either 2 or five – Nkd Nkd Oct 29 '15 at 13:05
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Titles such as "Finding the number of ways" do not describe the question accurately. A better title could be "Finding numbers which are composed of the digits 2 and 5". – Element118 Oct 29 '15 at 13:07
2 Answers
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You can have three $2$'s ($222$), two $2$'s and one $5$ ($225,252,522$), two $5$'s and one $2$ ($552,525,255$) and three $5$'s ($555$).
ANSWER: You will have $8$ such numbers.
EDIT: In standard permutation notation, you have $2$ choices for each digit, either $2$ or $5$. And in the given range, you will have $3$-digit numbers only. So total no. of numbers = $2 \times 2 \times 2 = 2^3 = 8$
SchrodingersCat
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$222$ and $555$ can appear only once as their interchanged digits are the same.
Now,one $2$ and two $5$'s can be arranged in $3!-(1+1+1)=3$ ways.$(why?)$
Also,two $2$ and one $5$ can be arranged in $3!-(1+1+1)=3$ ways.$(why?)$
So,total=$5+3+3=8$ ways.
If you can't answer "why?" mention in the comment,I will help you.
Soham
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