How many meaningful four-letter English words can be formed using the first, second, third, and sixth letters of the word "PROVIDE" (when counted from left to right), using each letter only once in each word?
- (a)One
- (b)Three
- (c)Two
- (d)Five
Answer
Why
Correct — B.
Rule: pick the letters by position, then test every arrangement.
PROVIDE: P(1) R(2) O(3) V(4) I(5) D(6) E(7).
The letters are P, R, O, D.
Words using P, R, O, D once each:
PROD (to poke), DROP and DORP (a village or small town, from Dutch).
Three words → option (b).
Why the others are wrong
- (a)One — One undercounts at once: PROD and DROP are both everyday words built from P, R, O and D, so the count is at least two.
- (c)Two — Two stops at PROD and DROP. A third arrangement, DORP, is a dictionary word for a village or small town, borrowed from Dutch.
- (d)Five — Five would need five real words among the 24 arrangements of P, R, O, D. Of these, only PROD, DROP and DORP are dictionary words.
Concept
These items have two steps. First, number the letters of the given word before choosing any: the sixth letter of PROVIDE is D, not E.
Second, list the arrangements systematically, for example by fixing the first letter. Four different letters give 4 × 3 × 2 × 1 = 24 orders, and three of them are words: PROD, DROP and DORP.
DORP is rare in everyday English, but it is a dictionary word: a noun meaning a village or small town, borrowed from Dutch and now used chiefly in South Africa. Without it the count would be two, and the key says three.
Key facts
- PROVIDE numbered: P1 R2 O3 V4 I5 D6 E7.
- Four different letters can be arranged in 4 × 3 × 2 × 1 = 24 ways.
- PROD means to poke, DROP means to let fall, and DORP means a village or small town.
Study next
Common traps
- Taking the sixth letter as E and working with P, R, O, E
- Stopping at the two everyday words and missing DORP
15 Sep 2025, 09:00, Reasoning Q.8 asks the same of the first four letters of CAMERA, C, A, M and E, and keys Three.
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