How many four-digit numbers can be formed from the digits 1 and 2 if repetitions are allowed?

Hi Caro,

Consider the four digit number digit-by-digit.

Digit one: two possibilities, 1 or 2.

Digit two: two possibilities, 1 or 2.

Digit three: two possibilities, 1 or 2.

Digit four: two possibilities, 1 or 2.

The total number of possibilities is the product of the possibilities of the digits.

Total possibilities = 2 * 2 * 2 * 2 = 2^4 = 16.

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More generally, an n-digit number with m possibilities for each digit will have:

Total possibilities = m^n.

For a variety to be divisible by ability of 11. Sum of wierd place numbers = sum of even place numbers As repetition is authorized thus, 1111 may be the 1st variety and 5555 may be the final variety. So sum of wierd place numbers or perhaps place numbers ranges from 2 (in 1111) to ten (in 5555). No. of numbers with sum 2 = a million No. of numbers with sum 3 = 4 a threat with digits a million and a pair of Numbers like 1122, 1221 , 2112, 2211. So 4 numbers. No. of numbers with sum 4 = 9 a threat with (2,2) and (a million,3) With (2,2) = a million basically ( 2222) With (a million,3) = 4 ( like in previous case) With (a million,3) and (2,2) = 4 ( 1232, 3212, 2123, 2321) No.of numbers with sum 5 = sixteen a threat with (a million,4), (2,3) and (a million,4,2,3). Now it follows a trend. LIke a million, 4, 9, sixteen, 25, sixteen, 9, 4, a million So answer = a million+4+9+sixteen+25+sixteen+9+4+a million = eighty 5 answer is E NONE of those

2^4

2*2*2*2

1111

1112

1121

1122

1211

1212

1221

1222

2111

2112

2121

2122

2211

2212

2221

2222

yup you answered it correctly

it's 16

Unit place can be filled by two given numbers = 2

Tenth place can be filled by two given numbers = 2

Hundredth place can be filled by two given numbers = 2

thousand place can be filled by two given numbers = 2

Therefore total number ways = 2x2x2x2 =2^4 =16 ways ................Ans

Using the BASIC COUNTING Principle, multiply

the number of choices (2) for EACH place holder (4)

___ x ___ x ___ x ___

_2_ x _2_ x _2_ x _2_ = 16

ANSWER.....16