A password of 4 letters is to be formed with vowels alone How many such passwords are possible if
(i) repetition of letters is allowed
(ii) repetition of letters is not allowed?
If $A$ denotes the outcome of (i) and $B$ denotes the outcome of (ii), then find the value of $A - B$ .

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Solution

The tasks $T_{1^{2}} T_{2^{3}} T_{3}$ AND $T_{4}$ are about filling the 1st, 2nd, 3rd and 4th slots in the password
(i) The first slot can be filled in 5 ways (a, e, i, o or u) The second can also be filled in 5 ways (with repetition being allowed)
The third and fourth can also be filled in 5 ways each
Using the generalization we get $5 \times 5 \times 5 \times 5 = 625$ passwords
$A = 625$
(ii) The first slot can be filled in 5 ways (a, e, i, o or u) The second slot can be filled in 4 ways (as repetition is not allowed)
The third and fourth in 3 and 2 ways respectively
Thus the total number of possible passwords are $5 \times 4 \times 3 \times 2 = 120$
$B = 120$

$A - B = 625 - 120 = 505$

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A password of 4 letters is to be formed with vowels alone How many such passwords are possible if(i) repetition of letters is allowed(ii) repetition of letters is not allowed?If A denotes the outcome of (i) and B denotes the outcome of (ii), then find the value of A−B.

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(i) repetition of letters is allowed
(ii) repetition of letters is not allowed?
If $A$ denotes the outcome of (i) and $B$ denotes the outcome of (ii), then find the value of $A - B$ .