Question

seven cards each bearing a letter can be arranged to spell the word "doubles".how many three letter code words can be formed from these cards

Answer 1

Answer:

Step-by-step explanation:

Here, we will use permutation

Therefore, 3 letter code words that can be formed out of 7 cards is 7P3=840 codes

Answer 2

The three letters code words can be formed from these cards = 210

Step-by-step explanation:

The given word = doubles and

The total number of letters = 7

To find, the three letters code words can be formed from these cards = ?

All letters are single times.

The three letters code words can be formed from these cards

$=^{7}P_{3}$

$=\dfrac{7!}{(7-3)!}$

[ ∵ $^{n}P_{r}=\dfrac{n!}{(n-r)!}$]

$=\dfrac{7!}{(4)!}$

$=\dfrac{4!\times 5\times 6 \times 7}{(4)!}$

$=5\times 6 \times 7$

= 210

Hence, the three letters code words can be formed from these cards = 210