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23 June, 13:56

Find the number of possible outcomes if the numbers 1 through 7 are written on different pieces of paper and placed in a hat. Two of these numbered pieces of paper are selected without replacement, and a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.

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  1. 23 June, 16:42
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    The number of the possible outcomes are:

    12,13,14,15,16,17

    21,23,24,25,26,27

    31,32,34,35,36,37

    41,42,43,45,46,47

    51,52,53,54,56,57

    61,62,63,64,65,67

    71,72,73,74,75,76

    The total number of possible outcomes = 42

    Step-by-step explanation:

    Given that:

    the numbers 1 through 7 are written on different pieces of paper; &

    Two of these numbered pieces of paper are selected without replacement;

    Also,

    a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.

    Then:

    if the first number drawn is 1, then the possible outcomes will be:

    12,13,14,15,16,17

    If the first number drawn is 2; then the possible outcomes will be:

    21,23,24,25,26,27

    If the first number drawn is 3; then the possible outcomes will be:

    31,32,34,35,36,37

    If the first number drawn is 4; then the possible outcomes will be:

    41,42,43,45,46,47

    If the first number drawn is 5; then the possible outcomes will be:

    51,52,53,54,56,57

    If the first number drawn is 6; then the possible outcomes will be:

    61,62,63,64,65,67

    If the first number drawn is 7; then the possible outcomes will be:

    71,72,73,74,75,76

    The number of the possible outcomes are:

    12,13,14,15,16,17

    21,23,24,25,26,27

    31,32,34,35,36,37

    41,42,43,45,46,47

    51,52,53,54,56,57

    61,62,63,64,65,67

    71,72,73,74,75,76

    The total number of possible outcomes = 7 * 6 = 42
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